% %ȉ̕RgƂ̂łC_ł͂܂ł܂B
% ̃^Cg
[Title]
303_data(1)

% 蕶
% Ȃ΁C[Level1]ɏ̂̂܂ܖ蕶ƂȂB
[Problem]
̖₢ɓB
% tHg̑傫B1`10C܂TeX̃R}hw肷B
% ftHǵC5i\normalsizej
% 1\tinyC 2\scriptsizeC3\footnotesizeC4\smallC 5\normalsize
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[FontSize]
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% vAuɒǉpbP[Wt@Cw肷B
[usepackage]
\usepackage{color,amssymb}
\usepackage{graphicx,pxrubrica}

% ꂼ̖𓚂$\displaystyle $tꍇ́C@ON ܂1
% ꂼ̖𓚂$\displaystyle $tȂꍇ́COFF܂0
% up̕ҏWv|u[U[ݒv̉ɂݒ
% @@@@@@@@@@@@@@@@@ꍇɎw肵ĂB
% LqȂ΁Cup̕ҏWv|u[U[ݒv
% @@@@@@@@@@@@@@@@@@@ɂݒ肪D悳܂B
[displaystyle]
OFF


% Level1̖BȉLevel7܂œlB
% 1sڂɂ͏ڍאݒ̃^CgB
% 2sڈȍ~ɖƂ̉𓚂B
% Ɖ𓚁C𓚂Ɩ͂PsďB
% vZߒꍇ́CƉ𓚂̊ԂɂPsԊuC
% ŏprocessƂsC̎̍svZߒĂB
[Level1]
f[^Ɠxz\
̃f[^́CNX20l̃eXgA̐тłB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccccccc|}
\hline
 $5$ & $5$ & $20$ & $30$ & $35$ & $35$ & $40$ & $50$ & $50$ & $50$ \\
 $60$ & $60$ & $60$ & $70$ & $75$ & $80$ & $80$ & $90$ & $90$ & $95$ \\
\hline
\end{tabular}\end{center}\end{table}}\\
̓xz\B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  K & Kl & x & Γx \\
  i_j&i_j&ilj& \\ \hline
 0ȏ20 & & & \\ \hline
 20ȏ40 & & & \\ \hline
 40ȏ60 & & & \\ \hline
 60ȏ80 & & & \\ \hline
 80ȏ100 & & & \\ \hline
 v         & ^ & & \\ \hline
\end{tabular}\end{center}\end{table}

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  K & Kl & x & Γx \\
  i_j&i_j&ilj& \\ \hline
 0ȏ20 & 10 & 2 & 0.1 \\ \hline
 20ȏ40 & 30 & 4 & 0.2 \\ \hline
 40ȏ60 & 50 & 4 & 0.2 \\ \hline
 60ȏ80 & 70 & 5 & 0.25 \\ \hline
 80ȏ100 & 90 & 5 & 0.25 \\ \hline
  v         & ^ & 20 & 1.0 \\ \hline
\end{tabular}\end{center}\end{table}

̓xz\́Cnh{[̋L^܂Ƃ߂̂łB
̓xz\ƂɁCqXgOȂB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  L^ & Kl & l & Γx \\
  imj&imj&ilj& \\ \hline
 10ȏ13 & 11.5 & 2 & 0.06 \\ \hline
 13ȏ16 & 14.5 & 8 & 0.22 \\ \hline
 16ȏ19 & 17.5 & 8 & 0.22 \\ \hline
 19ȏ22 & 20.5 & 9 & 0.25 \\ \hline
 22ȏ25 & 23.5 & 7 & 0.19 \\ \hline
 25ȏ28 & 26.5 & 2 & 0.06 \\ \hline
  v         & ^ & 36 & 1.0 \\ \hline
\end{tabular}\end{center} \end{table}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic104.tex}
\end{center}

\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic104p.tex}
\end{center}

̓xz\́CNX̐k̐g̕z܂Ƃ߂̂łB
̓xz\ƃqXgOȂB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  g & Kl & l & Γx \\
  icmj&icmj&ilj& \\ \hline
 130ȏ140 & 135 & 4 &  \\ \hline
 140ȏ150 & 145 & 12 &  \\ \hline
 150ȏ160 & 155 & 14 &  \\ \hline
 160ȏ170 & 165 & 14 &  \\ \hline
 170ȏ180 & 175 & 6 &  \\ \hline
  v         & ^ & 50 & 1.0 \\ \hline
\end{tabular}\end{center} \end{table}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic105.tex}
\end{center}

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  g & Kl & l & Γx \\
  icmj&icmj&ilj& \\ \hline
 130ȏ140 & 135 & 4 & 0.08 \\ \hline
 140ȏ150 & 145 & 12 & 0.24 \\ \hline
 150ȏ160 & 155 & 14 & 0.28 \\ \hline
 160ȏ170 & 165 & 14 & 0.28 \\ \hline
 170ȏ180 & 175 & 6 & 0.12 \\ \hline
  v         & ^ & 50 & 1.0 \\ \hline
\end{tabular}\end{center}\end{table}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic105p.tex}
\end{center}

̓xz\́CNX̐k̐g̕z܂Ƃ߂̂łB
̓xz\ƃqXgOȂB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  g & Kl & l & Γx \\
  icmj&icmj&ilj& \\ \hline
 130ȏ140 & 135 & 2 &  \\ \hline
 140ȏ150 & 145 & 8 &  \\ \hline
 150ȏ160 & 155 & 14 &  \\ \hline
 160ȏ170 & 165 & 10 &  \\ \hline
 170ȏ180 & 175 & 6 &  \\ \hline
  v         & ^ & 40 & 1.0 \\ \hline
\end{tabular}\end{center}\end{table}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic106.tex}
\end{center}

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  g & Kl & l & Γx \\
  icmj&icmj&ilj& \\ \hline
 130ȏ140 & 135 & 2 & 0.05 \\ \hline
 140ȏ150 & 145 & 8 & 0.20 \\ \hline
 150ȏ160 & 155 & 14 & 0.35 \\ \hline
 160ȏ170 & 165 & 10 & 0.25 \\ \hline
 170ȏ180 & 175 & 6 & 0.15 \\ \hline
  v         & ^ & 40 & 1.0 \\ \hline
\end{tabular}\end{center}\end{table}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic106p.tex}
\end{center}

̕\́CNX̐k30l50m̃^C𐮗̂ŁC
^C0.5bƂ̊Kɋ؂C̊Kɓl𒲂ׂ̂łB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|}
 \hline
  50m̃^C & l \\
  ibj@@@@&ilj \\ \hline
 7.0ȏ7.5 & 2 \\ \hline
 7.5ȏ8.0 & 4 \\ \hline
 8.0ȏ8.5 & 7 \\ \hline
 8.5ȏ9.0 & 11 \\ \hline
 9.0ȏ9.5 & 5 \\ \hline
 9.5ȏ10.0 & 1 \\ \hline
  v         & 30 \\ \hline
\end{tabular}\end{center}\end{table}\\
i1j9.0bȏ̐ĺCŜ̉\%B\\
i2jxz\ƂɂāCqXgOB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic107.tex}
\end{center}

process
i1j$\displaystyle\frac{6}{30}\times 100=20\%$\\

i1j20\% \\
i2j\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic107p.tex}
\end{center}

̕\́CNX50l̐g𒲂ׂđΓx̕z\ɂ̂łB
g160cmȏ165cm̐l͉l邩B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|}
 \hline
  g & Γx \\
  icmj& \\ \hline
 140ȏ145 & 0.10 \\ \hline
 145ȏ150 & 0.20 \\ \hline
 150ȏ155 & 0.28 \\ \hline
 155ȏ160 & 0.24 \\ \hline
 160ȏ165 &  \\ \hline
 165ȏ170 & 0.04 \\ \hline
  v         & 1.00 \\ \hline
\end{tabular}\end{center}\end{table}

process
160ȏ165̑Γx\\
$1-0.86=0.14$ƂȂ邩C\\
$50\times 0.14=7$l

7l

̕\́CNX50l̐g𒲂ׂđΓx̕z\ɂ̂łB
g150cmȏ155cm̐l͉l邩B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|}
 \hline
  g & Γx \\
  icmj& \\ \hline
 140ȏ145 & 0.10 \\ \hline
 145ȏ150 & 0.20 \\ \hline
 150ȏ155 &  \\ \hline
 155ȏ160 & 0.24 \\ \hline
 160ȏ165 & 0.14 \\ \hline
 165ȏ170 & 0.04 \\ \hline
  v         & 1.00 \\ \hline
\end{tabular}\end{center}\end{table}

process
150ȏ155̑Γx\\
$1-0.72=0.28$ƂȂ邩C\\
$50\times 0.28=14$l

14l

̕\́CNX50l̐g𒲂ׂđΓx̕z\ɂ̂łB
g165cmȏ170cm̐l͉l邩B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|}
 \hline
  g & Γx \\
  icmj& \\ \hline
 140ȏ145 & 0.10 \\ \hline
 145ȏ150 & 0.20 \\ \hline
 150ȏ155 & 0.28 \\ \hline
 155ȏ160 & 0.24 \\ \hline
 160ȏ165 & 0.14 \\ \hline
 165ȏ170 &  \\ \hline
  v         & 1.00 \\ \hline
\end{tabular}\end{center}\end{table}

process
165ȏ170̑Γx\\
$1-0.96=0.04$ƂȂ邩C\\
$50\times 0.04=2$l

2l

̕\́C钆wZ̐k80l̐т̋L^xz\ɐ̂łB
55cmȏ60cm̊K̑Γx߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|}
 \hline
  L^ & x \\
  icmj& ilj\\ \hline
 45ȏ50 & 5 \\ \hline
 50ȏ55 & 10 \\ \hline
 55ȏ60 & 24 \\ \hline
 60ȏ65 & 21 \\ \hline
 65ȏ70 & 19 \\ \hline
 70ȏ75 & 1 \\ \hline
  v         & 80 \\ \hline
\end{tabular}\end{center}\end{table}

process
$\displaystyle\frac{24}{80}=0.30$

$0.30$

̕\͂NX25lɂāCт̌ʂ܂Ƃ˂̂łB
45cmȏ50cm̊K̑Γx\fbox{\hspace{8pt} 19 \hspace{8pt}}
łB\\
\textcircled{\small 1}\,$0.12$~~~
\textcircled{\small 2}\,$0.16$~~~
\textcircled{\small 3}\,$0.2$~~~
\textcircled{\small 4}\,$0.36$\\
\begin{table}[!hbt]
\begin{center}\begin{tabular}{|c|c|}
\hline
 K(cm) & x(l)  \\ \hline \hline
 ȏ\hspace{8pt}  &  \\ \hline
 $30 \sim 35$ & $1$ \\ \hline
 $35 \sim 40$ & $2$ \\ \hline
 $40 \sim 45$ & $5$ \\ \hline
 $45 \sim 50$ & $9$ \\ \hline
 $50 \sim 55$ & $4$ \\ \hline
 $55 \sim 60$ & $3$ \\ \hline
 $60 \sim 65$ & $1$ \\ \hline \hline
 v & $25$ \\ \hline
\end{tabular}\end{center}\end{table}

process
$\displaystyle\frac{5}{25}=0.20$

\textcircled{\small 3}

̕\́CNX40lɑ΂čs͌̌ʂ܂Ƃ߂̂łB
l܂ފK̊Kl
\fbox{\hspace{8pt} 19 \hspace{8pt}}
kgłB\\
\textcircled{\small 1}\,$32.5$~~~
\textcircled{\small 2}\,$35$~~~
\textcircled{\small 3}\,$37.5$~~~
\textcircled{\small 4}\,$40$\\
\begin{table}[!hbt]
\begin{center}\begin{tabular}{|c|c|}
\hline
 K(cm) & x(l)  \\ \hline \hline
 ȏ\hspace{8pt}  &  \\ \hline
 $20 \sim 25$ & $2$ \\ \hline
 $25 \sim 30$ & $5$ \\ \hline
 $30 \sim 35$ & $9$ \\ \hline
 $35 \sim 40$ & $12$ \\ \hline
 $40 \sim 45$ & $6$ \\ \hline
 $45 \sim 50$ & $3$ \\ \hline
 $50 \sim 55$ & $3$ \\ \hline \hline
 v & $40$ \\ \hline
\end{tabular}\end{center}\end{table}

process
l܂ފK$35\sim 40$łB\\
$\displaystyle\frac{35+40}{2}=37.5$

\textcircled{\small 3}

E̕\́C鍂Z1Njq40l̐g𑪒肵ʂC
xz\ɕ\̂łB
170cmȏ̐l͑Ŝ
\fbox{\hspace{8pt} 19 \hspace{8pt}}$\%$łB\\
\textcircled{\small 1}\,$37.5$~~~
\textcircled{\small 2}\,$40$~~~
\textcircled{\small 3}\,$60$~~~
\textcircled{\small 4}\,$80$
\begin{table}[!hbt]
\begin{center}\begin{tabular}{|c|c|}
\hline
 Kicmj & xilj \\ \hline
 158ȏ162 & 2 \\ \hline
 162\hspace{6pt}$\sim$\hspace{6pt}166 & 5 \\ \hline
 166\hspace{6pt}$\sim$\hspace{6pt}170 & 9 \\ \hline
 170\hspace{6pt}$\sim$\hspace{6pt}174 & 15 \\ \hline
 174\hspace{6pt}$\sim$\hspace{6pt}178 & 8 \\ \hline
 178\hspace{6pt}$\sim$\hspace{6pt}182 & 1 \\ \hline
 v & 40 \\ \hline
\end{tabular}\end{center}\end{table}

process
$\displaystyle\frac{24}{40} \times 100=60$\%

\textcircled{\small 3}








[Level2]
ϒlClixz\j
̕\́C40l̃NXō̏eXgsƂ
ʂ܂Ƃ߂̂łB
̏eXg̕ϓ_͉_B
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 _ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10  \\ \hline
 l & $1$ & $1$ & $3$ & $4$ & $5$ & $3$ & $5$ & $8$ & $4$ & $4$ & $2$\\
\hline
\end{tabular}\end{center}\end{table}}

process
v_$=0\times 1+1\times 1+2\times 3+3\times 4+4\times 5+5\times 3
+6\times 5+7\times 8+8\times 4+9\times 10\times 2=228$\\
$228 \div 40=5.7$_

5.7_

̕\́Ck40l̂NX̐k̐g̓xz\łB
̕\Cg̕ϒl𐮐̒lŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  g & Kl & l & Kl \\
  icmj&icmj&ilj& $\times$l\\ \hline
 130ȏ140 &  & 2 &  \\ \hline
 140ȏ150 &  & 9 &  \\ \hline
 150ȏ160 &  & 13 &  \\ \hline
 160ȏ170 &  & 12 &  \\ \hline
 170ȏ180 &  & 4 &  \\ \hline
  v         & ^ & 40 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$6270 \div 40=156.75\fallingdotseq 157$cm

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  g & Kl & l & Kl \\
  icmj&icmj&ilj& $\times$l\\ \hline
 130ȏ140 & 135 & 2 & 270 \\ \hline
 140ȏ150 & 145 & 9 & 1305 \\ \hline
 150ȏ160 & 155 & 13 & 2015 \\ \hline
 160ȏ170 & 165 & 12 & 1980 \\ \hline
 170ȏ180 & 175 & 4 & 700 \\ \hline
  v         & ^ & 40 & 6270 \\ \hline
\end{tabular}\end{center}\end{table}\\
ϒl$=157$cm

̕\́Cnh{[̋L^̓xz\łB
̕\CL^̕ϒlƒl1ʂ܂ŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  L^ & Kl & l & Kl \\
  imj&imj&ilj& $\times$l\\ \hline
 10ȏ14 &  & 3 &  \\ \hline
 14ȏ18 &  & 8 &  \\ \hline
 18ȏ22 &  & 14 &  \\ \hline
 22ȏ26 &  & 20 &  \\ \hline
 26ȏ30 &  & 5 &  \\ \hline
  v        & ^ & 50 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$\displaystyle\frac{1064}{50}=21.28\fallingdotseq 21.3$m\\
l25lڂ̊Kl20mC
26lڂ̊Kl24mB
āC$\displaystyle\frac{20+24}{2}=22$m

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  L^ & Kl & l & Kl \\
  imj&imj&ilj& $\times$l\\ \hline
 10ȏ14 & 12 & 3 & 36 \\ \hline
 14ȏ18 & 16 & 8 & 128 \\ \hline
 18ȏ22 & 20 & 14 & 280 \\ \hline
 22ȏ26 & 24 & 20 & 480 \\ \hline
 26ȏ30 & 28 & 5 & 140 \\ \hline
  v         & ^ & 50 & 1064 \\ \hline
\end{tabular}\end{center}\end{table}
\\ϒl$=21.3$mCl$=22.0$m

̕\́Cnh{[̋L^̓xz\łB
̕\̕ϒl20mƂĊCL^̕ϒlƒl1ʂ܂ŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize L^} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeimj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 10ȏ14} & 12 & $-8$ & 3 &  \\ \hline
 {\scriptsize 14ȏ18} & 16 & & 8 &  \\ \hline
 {\scriptsize 18ȏ22} & 20 & & 14 &  \\ \hline
 {\scriptsize 22ȏ26} & 24 & & 20 &  \\ \hline
 {\scriptsize 26ȏ30} & 28 & & 5 &  \\ \hline
  v        & ^ & ^ & 50 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$20+\displaystyle\frac{64}{50}=20+1.28=21.28\fallingdotseq 21.3$m\\
l25lڂ̊Kl20mC
26lڂ̊Kl24mB
āC$\displaystyle\frac{20+24}{2}=22$m

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize L^} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeimj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 10ȏ14} & 12 & $-8$ & 3 & $-24$ \\ \hline
 {\scriptsize 14ȏ18} & 16 & $-4$ & 8 & $-32$ \\ \hline
 {\scriptsize 18ȏ22} & 20 & $0$ & 14 & 0 \\ \hline
 {\scriptsize 22ȏ26} & 24 & $4$ & 20 & 80 \\ \hline
 {\scriptsize 26ȏ30} & 28 & $8$ & 5 & 40 \\ \hline
  v        & ^ & ^ & 50 & 64 \\ \hline
\end{tabular}\end{center}\end{table}
 \\ ϒl$=21.3$mCl$=22.0$m

̕\́Cnh{[̋L^̓xz\łB
̕\̕ϒl20mƂĊCL^̕ϒlƒl1ʂ܂ŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize L^} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeimj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 16ȏ18} & 17 & $-3$ & 4 &  \\ \hline
 {\scriptsize 18ȏ20} & 19 &    & 6 &  \\ \hline
 {\scriptsize 20ȏ22} & 21 &    & 7 &  \\ \hline
 {\scriptsize 22ȏ24} & 23 &    & 2 &  \\ \hline
 {\scriptsize 24ȏ26} & 25 &    & 1 &  \\ \hline
  v        & ^ & ^ & 20 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$20+\displaystyle\frac{0}{20}=20+0=20.0$m\\
l10lڂ̊Kl19mC
11lڂ̊Kl21mB
āCl$=\displaystyle\frac{19+21}{2}=20$

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize L^} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeimj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 16ȏ18} & 17 & $-3$ & 4 & $-12$   \\ \hline
 {\scriptsize 18ȏ20} & 19 & $-1$ & 6 & $-6$ \\ \hline
 {\scriptsize 20ȏ22} & 21 & $1$  & 7 & $7$ \\ \hline
 {\scriptsize 22ȏ24} & 23 & $3$  & 2 & $6$ \\ \hline
 {\scriptsize 24ȏ26} & 25 & $5$   & 1 & $5$ \\ \hline
  v        & ^ & ^ & 20 & 0 \\ \hline
\end{tabular}\end{center}\end{table}
 \\ϒl$=20.0$mCl$=20.0$m

̕\́CNX̒jqk20l̐Ƃт̋L^C
xz\ɕ\̂łB
\̋𖄂߂āC20l̐Ƃт̕ϒl𐮐̒lŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  L^ & Kl & l & Kl \\
  icmj&icmj&ilj& $\times$l \\ \hline
 35ȏ40 &  & 2 &  \\ \hline
 40ȏ45 &  & 4 &  \\ \hline
 45ȏ50 &  & 7 &  \\ \hline
 50ȏ55 &  & 4 &  \\ \hline
 55ȏ60 &  & 3 &  \\ \hline
  v         & ^ & 20 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$960 \div 20=48$cm

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  L^ & Kl & l & Kl \\
  icmj&icmj&ilj& $\times$l \\ \hline
 35ȏ40 & 37.5 & 2 & 75.0 \\ \hline
 40ȏ45 & 42.5 & 4 & 170.0 \\ \hline
 45ȏ50 & 47.5 & 7 & 332.5 \\ \hline
 50ȏ55 & 52.5 & 4 & 210.0 \\ \hline
 55ȏ60 & 57.5 & 3 & 172.5 \\ \hline
  v         & ^ & 20 & 960.0 \\ \hline
\end{tabular}\end{center}\end{table}\\
ϒl$=48$cm

̕\́Ck20l̂NX̒jqk̐g̓xz\łB
̕\Cg̕ϒl_ȉ1̒l܂ŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  g & Kl & l & Kl \\
  icmj&icmj&ilj& $\times$l \\ \hline
 145.0ȏ150.0 &  & 1 &  \\ \hline
 150.0ȏ155.0 &  & 3 &  \\ \hline
 155.0ȏ160.0 &  & 6 &  \\ \hline
 160.0ȏ165.0 &  & 7 &  \\ \hline
 165.0ȏ170.0 &  & 3 &  \\ \hline
  v         & ^ & 20 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$3190 \div 20=159.5$cm

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  g & Kl & l & Kl \\
  icmj&icmj&ilj& $\times$l \\ \hline
 145.0ȏ150.0 & 147.5 & 1 & 147.5  \\ \hline
 150.0ȏ155.0 & 152.5 & 3 & 457.5 \\ \hline
 155.0ȏ160.0 & 157.5 & 6 & 945.0 \\ \hline
 160.0ȏ165.0 & 162.5 & 7 & 1137.5 \\ \hline
 165.0ȏ170.0 & 167.5 & 3 & 502.5 \\ \hline
  v         & ^ & 20 & 3190.0 \\ \hline
\end{tabular}\end{center}\end{table}\\
ϒl$=159.5$cm

̕\́CNX̏qk20l̐Ƃт̋L^xz\ɕ\̂łB
42.5̕ϒlƂĊC
20l̐Ƃт̕ϒl1ʂ܂ŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize L^} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeimj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 30ȏ35} &  &    & 2 &  \\ \hline
 {\scriptsize 35ȏ40} &  &    & 3 &  \\ \hline
 {\scriptsize 40ȏ45} &  &    & 4 &  \\ \hline
 {\scriptsize 45ȏ50} &  &    & 7 &  \\ \hline
 {\scriptsize 50ȏ55} &  &    & 4 &  \\ \hline
  v        & ^ & ^ & 20 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$42.5+\displaystyle\frac{40}{20}=42.5+2.0=44.5$m

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize L^} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeimj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 30ȏ35} & 32.5 &  $-10$  & 2 & $-20$ \\ \hline
 {\scriptsize 35ȏ40} & 37.5 &   $-5$ & 3 & $-15$ \\ \hline
 {\scriptsize 40ȏ45} & 42.5 &  0  & 4 & 0 \\ \hline
 {\scriptsize 45ȏ50} & 47.5 &  $5$  & 7 & 35 \\ \hline
 {\scriptsize 50ȏ55} & 52.5 &  $10$  & 4 & 40 \\ \hline
  v        & ^ & ^ & 20 & 40 \\ \hline
\end{tabular}\end{center} \end{table}\\
ϒl$=44.5$m

̕\́CNX̒jqk20l̑̏d̑茋ʂxz\ɕ\̂łB
̕\52.5kg̕ϒlƂĊC
̏d̕ϒl1ʂ܂ŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize ̏d} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeikgj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 40ȏ45} &  &    & 2 &  \\ \hline
 {\scriptsize 45ȏ50} &  &    & 4 &  \\ \hline
 {\scriptsize 50ȏ55} &  &    & 8 &  \\ \hline
 {\scriptsize 55ȏ60} &  &    & 5 &  \\ \hline
 {\scriptsize 60ȏ65} &  &    & 1 &  \\ \hline
  v        & ^ & ^ & 20 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$52.5+\displaystyle\frac{-5}{20}=52.5-0.25=52.25=52.25\fallingdotseq 52.3$m

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize ̏d} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeikgj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 40ȏ45} & 42.5 & $-10$   & 2 & $-20$ \\ \hline
 {\scriptsize 45ȏ50} & 47.5 &  $-5$  & 4 & $-20$ \\ \hline
 {\scriptsize 50ȏ55} & 52.5 &  0  & 8 & 0 \\ \hline
 {\scriptsize 55ȏ60} & 57.5 &  5  & 5 & 25 \\ \hline
 {\scriptsize 60ȏ65} & 62.5 &  10  & 1 & 10 \\ \hline
  v        & ^ & ^ & 20 & $-5$ \\ \hline
\end{tabular}\end{center}\end{table}\\
ϒl$=52.3$m

̕\́Ck20l̂NX̐k̒ʊwԂ̓xz\łB
̕\CʊwԂ̕ϒl𐮐̒lŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  ʊw & Kl & l & Kl \\
  ij&ij&ilj& $\times$l\\ \hline
 0ȏ10 &  & 3 &  \\ \hline
 10ȏ20 &  & 6 &  \\ \hline
 20ȏ30 &  & 8 &  \\ \hline
 30ȏ40 &  & 2 &  \\ \hline
 40ȏ50 &  & 1 &  \\ \hline
  v         & ^ & 20 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$420 \div 20=21$

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  ʊw & Kl & l & Kl \\
  ij&ij&ilj& $\times$l\\ \hline
 0ȏ10 & 5 & 3 & 15 \\ \hline
 10ȏ20 & 15 & 6 & 90 \\ \hline
 20ȏ30 & 25 & 8 & 200 \\ \hline
 30ȏ40 & 35 & 2 & 70 \\ \hline
 40ȏ50 & 45 & 1 & 45 \\ \hline
  v         & ^ & 20 & 420 \\ \hline
\end{tabular}\end{center}\end{table}\\
ϒl$=21$

̕\́Cnh{[̋L^̓xz\łB
̕\̕ϒl28mƂĊCL^̕ϒl߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize L^} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeimj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 20ȏ24} & 22 & $-6$ & 1 &  \\ \hline
 {\scriptsize 24ȏ28} & 26 & & 5 &  \\ \hline
 {\scriptsize 28ȏ32} & 30 & & 12 &  \\ \hline
 {\scriptsize 32ȏ36} & 34 & & 2 &  \\ \hline
  v        & ^ & ^ & 20 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$28+\displaystyle\frac{20}{20}=28+1=29$m\\

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize L^} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeimj}&{\scriptsizeimj}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 20ȏ24} & 22 & $-6$ & 1 & $-6$ \\ \hline
 {\scriptsize 24ȏ28} & 26 & $-2$ & 5 & $-10$ \\ \hline
 {\scriptsize 28ȏ32} & 30 & $2$ & 12 & $24$ \\ \hline
 {\scriptsize 32ȏ36} & 34 & $6$ & 2 & $12$ \\ \hline
  v        & ^ & ^ & 20 & 20 \\ \hline
\end{tabular}\end{center}\end{table}
 \\ ϒl$=29$m

̕\́Cw̐k10lIсCʊwԂ𒲂ׂēxz\ɐ̂łB
̕\CʊwԂ̕ϒl𐮐̒lŋ߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  ʊw & Kl & l & Kl \\
  ij&ij&ilj& $\times$l\\ \hline
 0ȏ10 &  & 2 &  \\ \hline
 10ȏ20 &  & 4 &  \\ \hline
 20ȏ30 &  & 3 &  \\ \hline
 30ȏ40 &  & 1 &  \\ \hline
  v         & ^ & 10 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$180 \div 10=18$

\begin{table}[htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  ʊw & Kl & l & Kl \\
  ij&ij&ilj& $\times$l\\ \hline
 0ȏ10 & 5 & 2 & 10 \\ \hline
 10ȏ20 & 15 & 4 & 60 \\ \hline
 20ȏ30 & 25 & 3 & 75 \\ \hline
 30ȏ40 & 35 & 1 & 35 \\ \hline
  v         & ^ & 10 & 180 \\ \hline
\end{tabular}\end{center}\end{table}\\
ϒl$=18$

̕\́Cw̏q20lɂĒʊwԂ𒲂ׂēxz\ɕ\̂łB
25̕ϒlƂĕ\C
ϒl߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize K} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeij}&{\scriptsizeij}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 0ȏ10} &  &    & 3 &  \\ \hline
 {\scriptsize 10ȏ20} &  &    & 6 &  \\ \hline
 {\scriptsize 20ȏ30} &  &    & 8 &  \\ \hline
 {\scriptsize 30ȏ40} &  &    & 2 &  \\ \hline
 {\scriptsize 40ȏ50} &  &    & 1 &  \\ \hline
  v        & ^ & ^ & 20 &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$25+\displaystyle\frac{-80}{20}=25-4=21$

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  {\scriptsize K} & {\scriptsize Kl} &  {\scriptsize Kl}     & {\scriptsize l} & {\scriptsize (Kl$-$} \\
  {\scriptsizeij}&{\scriptsizeij}   &  {\scriptsize $-$̕}   &{\scriptsizeilj}&  {\scriptsize )$\times$l} \\ \hline
 {\scriptsize 0ȏ10} & 5 &  $-20$  & 3 & $-60$ \\ \hline
 {\scriptsize 10ȏ20} & 15 &  $-10$  & 6 & $-60$ \\ \hline
 {\scriptsize 20ȏ30} & 25 &  $0$  & 8 & $0$ \\ \hline
 {\scriptsize 30ȏ40} & 35 &  $10$  & 2 & $20$ \\ \hline
 {\scriptsize 40ȏ50} & 45 &  $20$  & 1 & $20$ \\ \hline
  v        & ^ & ^ & 20 & $-80$ \\ \hline
\end{tabular}\end{center}\end{table}\\
ϒl$=21$

̕\́CNX̐k$20$l̃eXg̓_xz\ɕ\̂łB
ϒl߂\fbox{\hspace{8pt} 19 \hspace{8pt}}_łB\\
\textcircled{\small 1}\,$25$~~~
\textcircled{\small 2}\,$30$~~~
\textcircled{\small 3}\,$32$~~~
\textcircled{\small 4}\,$35$
\begin{table}[!hbt]
\begin{center}\begin{tabular}{|c|c|}
\hline
 K(cm) & x(l)  \\ \hline \hline
 ȏ\hspace{8pt}  &  \\ \hline
 $0 \sim 10$ & $1$ \\ \hline
 $10 \sim 20$ & $3$ \\ \hline
 $20 \sim 30$ & $5$ \\ \hline
 $30 \sim 40$ & $7$ \\ \hline
 $40 \sim 50$ & $4$ \\ \hline \hline
 v & $20$ \\ \hline
\end{tabular}\end{center}\end{table}

process
$\displaystyle\frac{5\times 1+15 \times 3+25\times 5 +35\times 7+45\times 4}{20}\\ =\displaystyle\frac{5+45+125+245+180}{20}=\displaystyle\frac{600}{20}=30$

\textcircled{\small 2}








[Level3]
lCϒlixz\Ȃj
f[^AF~~~
$4,\,8,\,1,\,2,\,8,\,7$\\
̒lƂēK؂Ȃ̂C
\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
\textcircled{\small 1}\,$4$~~~
\textcircled{\small 2}\,$4.5$~~~
\textcircled{\small 3}\,$5$~~~
\textcircled{\small 4}\,$5.5$~~~
\textcircled{\small 5}\,$6$

process
ɕׂƁC
$1,\,2,\,4,\,7,\,8,\,8$\\
l$=(4+7)/2=5.5$

\textcircled{\small 4}

f[^AF
~~~$5,\,2,\,1,\,9,\,6,\,4$\\
̕ϒlƒlƂēK؂Ȃ̂C
\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
\textcircled{\small 1}\,ϒl$4$Cl$4.5$~~
\textcircled{\small 2}\,ϒl$4.5$Cl$4$\\
\textcircled{\small 3}\,ϒl$4.5$Cl$4.5$~~
\textcircled{\small 4}\,ϒl$4.5$Cl$5$\\
\textcircled{\small 5}\,ϒl$5$Cl$4.5$

process
ɕׂƁC$1,\,2,\,4,\,5,\,6,\,9$\\
ϒl$=27/6=9/2=4.5$Cl$=(4+5)/2=4.5$

\textcircled{\small 3}

f[^AF~~
$1,\,1,\,2,\,2,\,2,\,2,\,3,\,3,\,3,\,4$\\
̒lƂēK؂Ȃ̂C
\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
\textcircled{\small 1}\,$1.5$~~~
\textcircled{\small 2}\,$2$~~~
\textcircled{\small 3}\,$2.5$~~~
\textcircled{\small 4}\,$3$~~~
\textcircled{\small 5}\,$3.5$

\textcircled{\small 2}

f[^AF~~~
$8,\,5,\,19,\,2,\,12$\\
̒lƂēK؂Ȃ̂C
\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
\textcircled{\small 1}\,$5$~~~
\textcircled{\small 2}\,$6.5$~~~
\textcircled{\small 3}\,$8$~~~
\textcircled{\small 4}\,$10$~~~
\textcircled{\small 5}\,$12$

process
ɕׂƁC
$2,\,5,\,8,\,12,\,19$\\

\textcircled{\small 3}

ϒl$5.0$ł鎟̃f[^ɂāC̊eɓȂB\\
f[^F$2,\,4,\,5,\,a,\,7,\,4$\\
$\rm(\,I\,)$\,$a$̒l$a=$\fbox{\hspace{8pt} 18 \hspace{8pt}}łB\\
$\rm(I\hspace{-.01em}I)$\,l\fbox{\hspace{8pt} 19 \hspace{8pt}}łB

process
$\rm(\,I\,)$\,$22+a=5 \times 6$\\
$x=30-22=8$\\
$\rm(I\hspace{-.01em}I)$\,ɕׂƁC\\
$2,\,4,\,4,\,5,\,7,\,8$\\
ł邩Cl$4.5$

$\rm(\,I\,)$\,$6$C$\rm(I\hspace{-.01em}I)$\,$4.5$

ϒl5ł鎟̃f[^ɂāC̊eɓȂB\\
$4,\,6,\,x,\,2,\,7,\,1,\,8$\\
$\rm(\,I\,)$\,$x$̒l$x=$\fbox{\hspace{8pt} 18 \hspace{8pt}}łB\\
$\rm(I\hspace{-.01em}I)$\,l\fbox{\hspace{8pt} 19 \hspace{8pt}}łB

process
$\rm(\,I\,)$\,$28+x=5 \times 7$\\
$x=35-28=7$\\
$\rm(I\hspace{-.01em}I)$\,ɕׂƁC\\
$1,\,2,\,4,\,6,\,7,\,7,\,8$\\
ł邩Cl$6$

$\rm(\,I\,)$\,$7$C$\rm(I\hspace{-.01em}I)$\,$6$

̃f[^́C16l̐k100__̃eXgsʂCl̏ɕׂ̂łB
̒l
\fbox{\hspace{8pt} 19 \hspace{8pt}}łB\\
$35$C$37$C
$40$C$42$C
$48$C$51$C
$54$C$56$C
$63$C$68$C
$69$C$74$C
$75$C$79$C
$85$C$88$i_j\\
\textcircled{\small 1}\,$56$~~~
\textcircled{\small 2}\,$59.5$~~~
\textcircled{\small 3}\,$63$~~~
\textcircled{\small 4}\,$65.5$

process
$\displaystyle\frac{56+63}{2}=59.5$

\textcircled{\small 2}

̎́CNX̒jqk20lnh{[Ƃ̂ꂼ̋L^imĵłB
̋L^jqk20l̃nh{[̋L^̕ϒl߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccccccc|}
\hline
 $18$ & $21$ & $20$ & $16$ & $22$ & $20$ & $21$ & $19$ & $18$ & $16$ \\
 $18$ & $25$ & $19$ & $20$ & $22$ & $17$ & $21$ & $18$ & $20$ & $17$ \\
\hline
\end{tabular}\end{center}\end{table}

process
̕ϒl20ƂƁCuL^$-$̕ϒlv͉̂悤łB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccccccc|}
\hline
$-2$ & $1$ & $0$ & $-4$ & $2$ & $0$ & $1$ & $-1$ & $-2$ & $-4$ \\
$-2$ & $5$ & $-1$ & $0$ & $2$ & $-3$ & $1$ & $-2$ & $0$ & $-3$ \\
\hline
\end{tabular}\end{center}\end{table}\\
$20+\displaystyle\frac{-12}{20}=20-0.6=19.4$

19.4m

̕\́CTbJ[`[̍ŋ߂20̓_̋L^܂Ƃ߂̂łB\\
i1jϒl\,ƁCi2jl\,߂B
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
 \hline
  _i_j & 0 & 1 & 2 & 3 & 4 & v \\ \hline
  xij& 5 & 6 & 8 & 0 & 1 & 20 \\ \hline
\end{tabular}\end{center}\end{table}

process
i1j$ϓ_=\displaystyle\frac{_}{}\\
=\displaystyle\frac{0\times 5+1\times 6+2\times 8+3\times 0+4\times 1}{20}\\
=\displaystyle\frac{26}{20}=1.3$_\\
i2j20ijȂ̂10Ԗڂ11Ԗڂ̓_̕ς߂΂悢B\\
_͉̂悤ł邩\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
  f[^ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7\\ \hline
  _i_j & 0 & 0 & 0 & 0 & 0 & 1 & 1\\ \hline \hline
  f[^ԍ & 8 & 9 & 10 & 11 & 12 &13& $\cdots$ \\ \hline
  _i_j & 1 & 1 & 1  & 1  & 2 & 2 & $\cdots$ \\ \hline
\end{tabular}\end{center}\end{table}

 i1j1.3_Ci2j1_

\hspace{8pt} 
E̐}́C10__̊eXgł20l̓_̃f[^
qXgOɕ\̂łB\\
\hspace{8pt} ̃f[^̍ŕpl\fbox{\bf\, A \,}i_jłC
l\fbox{\bf\, C \,}i_jłB\\
\hspace{8pt} \textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,$5.5$~~~
\textcircled{\small 2}\,$5$~~~
\textcircled{\small 3}\,$4.5$~~~
\textcircled{\small 4}\,$4$
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2801m601.eps}
 \end{center}\end{figure} 

{\bf A}F\textcircled{\small 4}C{\bf C}F\textcircled{\small 3}

̕\́C}\10km̕ɏoꂵ7l̋L^\̂łB\\
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline
    {\scriptsize I} & {\scriptsize AN} & {\scriptsize BN} & {\scriptsize CN} & {\scriptsize DN} & {\scriptsize EN} & {\scriptsize FN} & {\scriptsize GN} \\ \hline
    {\scriptsize L^} & 62 & 41 & 53 & 52 & 57 & 50 & 70 \\
    {\scriptsize ij} &       &     &      &      &     &      & \\ 
 \hline
  \end{tabular}\end{center}
\end{table} \\
\hspace{8pt} ̕\̃f[^ɂĂ̋LqƂ{\bf Ă}\fbox{\,A\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\textcircled{\small 1}\,ŏl41łB~~~
\textcircled{\small 2}\,ϒl55łB\\
\textcircled{\small 3}\,l52łB~~~
\textcircled{\small 4}\,͈͂29łB

process
f[^̏ɕׂƁC\\
41~~~50~~~52~~~53~~~57~~~62~~~70\\
l53łB

\textcircled{\small 3}

̕\́C鍂Z1N10lɂă{[̋L^lɕёւĕ\̂łBl߂B
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|c||c|c|c|c|c|c|c|c|c|c|} \hline
    {\footnotesize o}  & {\footnotesize 3} & {\footnotesize 10} & {\footnotesize 6} & {\footnotesize 7} & {\footnotesize 1} & {\footnotesize 8} & {\footnotesize 5} & {\footnotesize 2} & {\footnotesize 9} & {\footnotesize 4}  \\
    {\footnotesize ԍ} &  &  &  &  &  &  &  &  &  &  \\  \hline
    {\footnotesize i_j} & {\footnotesize 10} & {\footnotesize 13} & {\footnotesize 15} & {\footnotesize 17} & {\footnotesize 20} & {\footnotesize 21} & {\footnotesize 26} & {\footnotesize 28} & {\footnotesize 29} & {\footnotesize 31} \\ \hline
  \end{tabular}\end{center}
\end{table}

20.5

̃qXgÓCt@~[Xg𗘗p
30gɂāC1gƂ̐l𒲂ׂʂłB\\
\hspace{8pt} 
̃f[^̍ŕplClCϒl̑g
ƂĐ̂\fbox{\bf\, A \,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂IׁB
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|c||c|c|c|c|} \hline
               & \textcircled{\small 1} & \textcircled{\small 2} & \textcircled{\small 3} & \textcircled{\small 4} \\\hline\hline
      ŕpl & 2l & 2l & 6l & 6l \\ \hline
     l & 2l & 3l & 2l & 3l \\ \hline
       ϒl & 2.5l & 3l & 2.5l & 3l \\ \hline 
  \end{tabular}\end{center}
\end{table}

process
ŕpl$=2$Cl$=2$C
ϒl\\
$\displaystyle\frac{1\times 7+2\times 10+3\times 8+4\times 3+6\times 2}{30}=2.5$

\textcircled{\small 1}

8l̓_\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccccc|}
\hline
 $4$ & $4$ & $4$ & $4$ & $5$ & $5$ & $5$ & $9$ \\
\hline
\end{tabular}\end{center}\end{table} \\
̂ƂC\\
i1jϒl߂Bi2jl߂B\\
i3jŕpl߂Bi4j͈͂߂B

process
i1j$\overline x=\displaystyle\frac{40}{8}=5$\\
i2j$\displaystyle\frac{4+5}{2}=4.5$\\
i3j4Ci4j$9-4=5$

i1j5Ci2j4.5Ci3j4Ci4j5

9l̓_\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccccc|}
\hline
 $1$ & $2$ & $2$ & $3$ & $5$ & $5$ & $5$ & $6$ & $7$\\
\hline
\end{tabular}\end{center}\end{table}\\
̂ƂC\\
i1jϒl߂Bi2jl߂B\\
i3jŕpl߂Bi4j͈͂߂B

process
i1j$\overline x=\displaystyle\frac{36}{9}=4$\\
i2j$5$\\
i3j5Ci4j$7-1=6$

i1j4Ci2j5Ci3j5Ci4j6

5l̃eXg̓_\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 $3$ & $4$ & $4$ & $6$ & $a$ \\
\hline
\end{tabular}\end{center}\end{table}\\
łB\\
i1jϒl4_̂ƂC$a$̒l߂B\\
i2ji1ĵƂCl߂B

process
i1j$\displaystyle\frac{17+a}{5}=4$C$a=3$\\
i2j_ׂƁC\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 $3$ & $3$ & $4$ & $4$ & $6$ \\
\hline
\end{tabular}\end{center}\end{table}\\
ƂȂ邩Cl$=4$

i1j3Ci2j4

8l̓_\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccccc|}
\hline
 $3$ & $4$ & $4$ & $5$ & $5$ & $6$ & $7$ & $b$ \\
\hline
\end{tabular}\end{center}\end{table}\\
̂ƂC\\
i1jϒl5_̂ƂC$b$߂B\\
i2ji1ĵƂCl߂B\\

process
i1j$34+b=5\times 8=40$C$b=6$\\
i2jёւƁC\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccccc|}
\hline
 $3$ & $4$ & $4$ & $5$ & $5$ & $6$ & $6$ & $7$ \\
\hline
\end{tabular}\end{center}\end{table}\\
ł邩Cl5_

i1j$b=6$Ci2j5

̃f[^́CTbJ[`[̍ŋ߂20ł̓_łB\\
1,\,1,\,2,\,1,\,1,\,3,\,4,\,1,\,2,\,1,\,0,\,1,\,0,\,0,\,1,\,0,\,1,\,0,\,1,\,1i_j
_̕ϒlƁCŕpl̑gŐ̂\fbox{\bf\,A\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\textcircled{\small 1}\,ϒl1Cŕpl0\\
\textcircled{\small 2}\,ϒl1Cŕpl1\\
\textcircled{\small 3}\,ϒl1.1Cŕpl0\\
\textcircled{\small 4}\,ϒl1.1Cŕpl1

process
ϒl$=\displaystyle\frac{1\times 11+2\times 2+3\times 1+4\times 1}{20}=\displaystyle\frac{22}{20}$

\textcircled{\small 4}

̃f[^́Cu[x[̎̎nʂ5{̖؂Œׂ̂łB\\
\hspace{20pt}$4, 7, 11, 10, 8$\\
\textcircled{\small 1}\,l8(kg)łB\\
\textcircled{\small 2}\,ϒl8(kg)łB\\
\textcircled{\small 3}\,͈͂7(kg)łB\\
\textcircled{\small 4}\,1lʐ7.5(kg)łB

process
ɕׂƁC$4, 7, 8, 10, 11$\\
$Q_1=\displaystyle\frac{11}{2}=5.5$

\textcircled{\small 4}

4̐lȂf[^$102$C$121$C$135$CX̕ϒl$118$łƂB
$X=$\fbox{\hspace{8pt} 19 \hspace{8pt}}łB\\
\textcircled{\small 1}\,$113$~~~
\textcircled{\small 2}\,$114$~~~
\textcircled{\small 3}\,$115$~~~
\textcircled{\small 6}\,$116$

process
$100$̕ƁC\\
$2+21+35+x=18\times 4$\\
$58+x=72$~~~
$\therefore x=14$\\
$X=114$

\textcircled{\small 2}

̃f[^́CeXg13l̐k̓_łB
l\fbox{\hspace{8pt} 18 \hspace{8pt}}łB\\
if[^j\\
$52,\,67,\,57,\,68,\,78,\,94,\,74,\,46,\,83,\,71,\,65,\,66,\,63$\\
\textcircled{\small 1}\,$65$~~~
\textcircled{\small 2}\,$66$~~~
\textcircled{\small 3}\,$67$~~~
\textcircled{\small 4}\,$68$

process
ɕׂƁC\\
$46,\,52,\,57,\,63,\,65,\,66,\,67,\,68,\,71,\,74,\,78,\,83,\,94$\\
l$67$

\textcircled{\small 3}

̃f[^́C鍂Z̒jq10l̃nh{[̋L^\̂łB
̃f[^̒l\fbox{\hspace{8pt} 19 \hspace{8pt}}młB\\
$20,\hspace{4pt} 23,\hspace{4pt} 24,\hspace{4pt} 24,\hspace{4pt} 26,\hspace{4pt} 29,\hspace{4pt} 30,\hspace{4pt} 30,\hspace{4pt} 32,\hspace{4pt} 33$(m)\\
\textcircled{\small 1}\,$25$~~~
\textcircled{\small 2}\,$26$~~~
\textcircled{\small 3}\,$27.5$~~~
\textcircled{\small 4}\,$29$

process
$\displaystyle\frac{26+29}{2}=27.5$

\textcircled{\small 3}

$91,\,76,\,33,\,29,\,8,\,98,\,66,\,50,\,74,\,96$
̒l\fbox{\hspace{8pt} 18 \hspace{8pt}}łB\\
\textcircled{\small 1}\,$58$~~~
\textcircled{\small 2}\,$66$~~~
\textcircled{\small 3}\,$70$~~~
\textcircled{\small 4}\,$74$

process
ɕׂƁC
$8,\,29,\,33,\,50,\,66,\,74,\,76,\,91,\,96,\,98$
l$\displaystyle\frac{66+74}{2}=70$

\textcircled{\small 3}

\hspace{8pt}
鍂Z̕Ղł́CN{eBAƂăybg{g̃LbvW߂ĂB
̃f[^́CW܂Lbv̏dʂ5NL^̂łB\\
$1.3$~~~$2.4$~~~$2.8$~~~$3.0$~~~$2.5$ikgj\\
\hspace{8pt}
̃f[^̒l\fbox{\,\bf A\,}ikgjłCϒl\fbox{\,\bf C\,}ikgjłB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂琳̂IׁB\\
\textcircled{\small 1}\,$2.0$~~~
\textcircled{\small 2}\,$2.4$~~~
\textcircled{\small 3}\,$2.5$~~~
\textcircled{\small 4}\,$2.8$

process
ɕׂƁC\\
$1.3$~~~$2.4$~~~$2.5$~~~$2.8$~~~$3.0$ikgj\\
ϒl$\displaystyle\frac{12}{5}=2.4$

\fbox{\,\bf A\,}:\textcircled{\small 3}C\fbox{\,\bf C\,}:\textcircled{\small 2}

̃f[^́C8̒n1ԂɋNCŽʎ̂
łB\\
~~~$43,\,39,\,19,\,34,\,27,\,43,\,15,\,28$ij\\
̃f[^ɂĂ̋LqƂ{\bf Ă}\fbox{\bf\hspace{8pt} A \hspace{8pt}}
łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\textcircled{\small 1}\,l34ijłB\\
\textcircled{\small 2}\,ϒl31ijłB\\
\textcircled{\small 3}\,ŕpl43ijłB\\
\textcircled{\small 4}\,͈͂28ijłB

process
ɂƁC\\
~~~$15,\,19,\,27,\,28,\,34,\,39,\,43,\,43$ij\\
l$\displaystyle\frac{28+34}{2}=31$

\textcircled{\small 1}

|̑I10l4{\ruby{}{}āC
\ruby{I}{܂}ɂĖ{L^B
E̐}́C10l̋L^̃f[^qXgOɕ\̂łB
̃f[^̍ŕplƒl̑g
\fbox{\bf\hspace{4pt} A \hspace{8pt}}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,ŕpl3i{jCl2i{j\\
\textcircled{\small 2}\,ŕpl3i{jCl3i{j\\
\textcircled{\small 3}\,ŕpl5i{jCl2i{j\\
\textcircled{\small 4}\,ŕpl5i{jCl3i{j
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=40mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h3101601.eps}
 \end{center}\end{figure} 

\textcircled{\small 2}

̃f[^́C싅`[́C7l̓̏oꎎłB\\
$21,\,22,\,3,\,61,\,4,\,18,\,53$ij\\
̃f[^̒l\fbox{\bf\, AC \,}ijŁCϒl
\fbox{\bf\, EG \,}ijłB

process
ɕׂƁC\\
$3,\,4,\,18,\,21,\,22,\,53,\,61$\\
l$21$Cϒl
$\displaystyle\frac{182}{7}=26$

ACF$21$CEGF$26$

ϒl$5.3$ł鎟10̐l̃f[^ɂāC
̊eɓȂB\\
$4,\, 9,\, x,\, 5,\, 3,\, 8,\, 3,\, 6,\, 2,\, 6$\\
$\rm(\,I\,)$\,$x$̒l$x=$\fbox{\,19\,}łB\\
$\rm(I\hspace{-.01em}I)$\,l\fbox{\,20$.$21\,}łB

process
$46+x=53$~~~
$x=53-46=7$\\
l̏ɕׂƁC\\
$2,\, 3,\, 3,\, 4,\, 5,\, 6,\, 6,\, 7,\, 8,\, 9$\\
ł邩Cl$5.5$

$x=7$Cl$5.5$






[Level4]
PlʐC3lʐ
̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$Clʔ͈͂߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccc|}
\hline
 f[^ԍ &   1 &  2  &  3  & 4   &  5  &  6   & 7   \\ \hline
 f[^     & $2$ & $3$ & $8$ & $8$ & $9$ & $11$ & $15$ \\
\hline
\end{tabular}\end{center}\end{table}

$Q_1=3$,\,$Q_2=8$,\,$Q_3=11$C\\
$lʔ͈=Q_3-Q_1=11-3=8$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$Clʔ͈͂߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccc|}
\hline
 $4$ & $8$ & $6$ & $5$ & $2$ & $9$ \\
\hline
\end{tabular}\end{center}\end{table}

process
ёւ\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccc|}
\hline
 f[^ԍ &   1 &  2  &  3  & 4   &  5  &  6   \\ \hline
 f[^     & 2 & 4 & 5 & 6 & 8 & 9 \\
\hline
\end{tabular}\end{center}\end{table}

$Q_1=4$,\,$Q_2=5.5$,\,$Q_3=8$C\\
$lʔ͈=Q_3-Q_1=8-4=4$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$Clʔ͈͂߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccccc|}
\hline
 $7$ & $6$ & $8$ & $1$ & $3$ & $4$ & $2$ & $9$ \\
\hline
\end{tabular}\end{center}\end{table}

process
ёւ\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccc|}
\hline
 f[^ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8  \\ \hline
 f[^     & 1 & 2 & 3 & 4 & 6 & 7 & 8 & 9 \\
\hline
\end{tabular}\end{center}\end{table}\\
$Q_1=\displaystyle\frac{2+3}{2}=2.5$,\,
$Q_2=\displaystyle\frac{4+6}{2}=5$C\\
$Q_3=\displaystyle\frac{7+8}{2}=7.5$C\\
$Q_3-Q_1=7.5-2.5=5$

$Q_1=2.5$,\,$Q_2=5$,\,$Q_3=7.5$C$lʔ͈=5$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8  \\ \hline
 f[^     & 11 & 11 & 12 & 16 & 16 & 16 & 18 & 18 \\ \hline \hline
 f[^ԍ & 9  & 10  & 11  & 12  & 13  & 14  & 15  & ^  \\ \hline
 f[^     & 19 & 20 & 20 & 20 & 22 & 23 & 24 & ^ \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=16$,\,$Q_2=18$,\,$Q_3=20$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8  \\ \hline
 f[^     & 10 & 11 & 11 & 13 & 14 & 18 & 20 & 21 \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=11$,\,$Q_2=13.5$,\,$Q_3=19$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 & 9  \\ \hline
 f[^     & 3 & 4 & 6 & 8 & 9 & 9 & 10 & 12 & 15 \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=5$,\,$Q_2=9$,\,$Q_3=11$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  \\ \hline
 f[^     & 3 & 4 & 6 & 8 & 9 & 10 & 13 \\ \hline
\end{tabular}\end{center}\end{table}

$Q_1=4$,\,$Q_2=8$,\,$Q_3=10$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 & 9 & 10 \\ \hline
 f[^     & 3 & 4 & 6 & 8 & 9 & 10 & 11 & 12 & 14 & 17 \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=6$,\,$Q_2=9.5$,\,$Q_3=12$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7 & 8 \\ \hline
 f[^     & 3 & 5 & 6 & 8 & 9 & 9 & 11 & 14 \\ \hline
\end{tabular}\end{center}\end{table}

$Q_1=5.5$,\,$Q_2=8.5$,\,$Q_3=10$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8  \\ \hline
 f[^     & 0  & 2  & 3  & 4  & 5  & 6  & 6  & 7 \\ \hline
\end{tabular}\end{center}\end{table}

$Q_1=2.5$,\,$Q_2=4.5$,\,$Q_3=6$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\small 
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 \\ \hline
 f[^     & 1  & 2  & 2  & 3  & 4  & 4  & 4  & 5 \\ \hline \hline
 f[^ԍ & 9 & 10 & 11 & 12 & 13 & 14 & 15 & ^  \\ \hline
 f[^     & 6 & 6 & 7 & 8 & 9 & 10 & 10 & ^\\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=3$,\,$Q_2=5$,\,$Q_3=8$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 & 9  \\ \hline
 f[^     & 0 & 1 & 2 & 4 & 5 & 7 & 9 & 11 & 12 \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=1.5$,\,$Q_2=5$,\,$Q_3=10$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 & 9  \\ \hline
 f[^     & 1 & 4 & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=5.5$,\,$Q_2=9$,\,$Q_3=11.5$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7 & 8 & 9\\ \hline
 f[^     & 1 & 2 & 4 & 5 & 5 & 7 & 8 & 10 & 12\\ \hline
\end{tabular}\end{center}\end{table}

$Q_1=3$,\,$Q_2=5$,\,$Q_3=9$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7 \\ \hline
 f[^     & 1 & 1 & 2 & 3 & 3 & 4 & 4 \\ \hline
\end{tabular}\end{center}\end{table}

$Q_1=1$,\,$Q_2=3$,\,$Q_3=4$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7 & 8 \\ \hline
 f[^     & 2 & 3 & 3 & 3 & 5 & 5 & 7 & 8 \\ \hline
\end{tabular}\end{center}\end{table}

$Q_1=3$,\,$Q_2=4$,\,$Q_3=6$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7 & 8 & 9 & 10\\ \hline
 f[^     & 3 & 4 & 4 & 5 & 5 & 7 & 8 & 10 & 11 & 13\\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=4$,\,$Q_2=6$,\,$Q_3=10$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\scriptsize
\begin{table}[!h]
\begin{center}\begin{tabular}{|c|cccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7 & 8 & 9 & 10\\ \hline
 f[^     & 3 & 4 & 5 & 6 & 6 & 7 & 7 & 7 & 7 & 8\\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=5$,\,$Q_2=6.5$,\,$Q_3=7$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7 & 8 & 9 & 10\\ \hline
 f[^     & 2 & 3 & 4 & 5 & 6 & 7 & 7 & 8 & 9 & 9\\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=4$,\,$Q_2=6.5$,\,$Q_3=8$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 & 9  \\ \hline
 f[^     & 3 & 4 & 6 & 7 & 8 & 12 & 14 & 15 & 17 \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=5$,\,$Q_2=8$,\,$Q_3=14.5$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 & 9  \\ \hline
 f[^     & 12 & 16 & 21 & 23 & 27 & 33 & 36 & 41 & 50 \\ \hline
\end{tabular}\end{center}\end{table}}

process
$Q_1=\displaystyle\frac{16+21}{2}=\displaystyle\frac{37}{2}=18.5$C\\
$Q_3=\displaystyle\frac{36+41}{2}=\displaystyle\frac{77}{2}=38.5$

$Q_1=18.5$,\,$Q_2=27$,\,$Q_3=38.5$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 & 9 & 10 \\ \hline
 f[^     & 15 & 18 & 21 & 33 & 38 & 40 & 55 & 61 & 69 & 75 \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=21$,\,$Q_2=39$,\,$Q_3=61$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 & 9 & 10 \\ \hline
 f[^     & 2 & 3 & 4 & 7 & 8 & 8 & 9 & 9 & 10 & 10 \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=4$,\,$Q_2=8$,\,$Q_3=9$

̃f[^̑1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|cccccccccc|}
\hline
 f[^ԍ & 1  & 2  & 3  & 4  & 5  & 6  & 7  & 8 & 9 & 10 \\ \hline
 f[^     & 5 & 5 & 5 & 7 & 7 & 7 & 7 & 8 & 9 & 10 \\ \hline
\end{tabular}\end{center}\end{table}}

$Q_1=5$,\,$Q_2=7$,\,$Q_3=8$








[Level5]
Ђ}
̃f[^́CAI̍ŋ10̃oXPbg{[̎ŋ_Ⴂɕׂ̂łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  &  &  &  &   \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10  \\ \hline
 _ & $10$ & $14$ & $16$ & $16$ & $16$ & $18$ & $18$ & $22$ & $24$ & $26$\\
\hline
\end{tabular}\end{center}\end{table}}
 \\̃f[^ɂāC̒lꂼꋁ߁CЂ}Biϒl$+$ŋLj\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
 ϒl & 1    & l & 3      & ͈ & l \\ 
  @    &  lʐ &     & lʐ &  @@&  ͈ \\ \hline
        &        &           &          &      &       \\
        &        &           &          &      &       \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic101.tex}
\end{center}

process
\textcircled{\small 1}ϒl$=\displaystyle\frac{180}{10}=18$\\
\textcircled{\small 2}1lʐ$=16$\\
\textcircled{\small 3}li2lʐj$=\displaystyle\frac{16+18}{2}=17$\\
\textcircled{\small 4}3lʐ$=22$\\
\textcircled{\small 5}͈́iWj$=iőlj-iŏlj=26-10=16$\\
\textcircled{\small 6}lʔ͈$=i3lʐj-i1lʐj=22-16=6$

{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
 ϒl & 1 & l & 3      & ͈ & l \\ 
  @    & lʐ &   & lʐ &  @@&  ͈ \\ \hline
        &        &           &          &      &       \\
   18 & 16   & 17      & 22     & 16 & 6   \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic101p.tex}
\end{center}

̃f[^́CBI̍ŋ10̃oXPbg{[̎ŋ_Ⴂɕׂ̂łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  &  &  &  &   \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10  \\ \hline
 _ & $4$ & $6$ & $10$ & $14$ & $14$ & $20$ & $24$ & $28$ & $30$ & $30$\\
\hline
\end{tabular}\end{center}\end{table}
}
 \\̃f[^ɂāC̒lꂼꋁ߁CЂ}Biϒl$+$ŋLj\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
 ϒl &  1 & l & 3      & ͈ & l \\ 
  @    & lʐ &   & lʐ &  @@&  ͈ \\ \hline
        &        &           &          &      &       \\
        &        &           &          &      &       \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic102.tex}
\end{center}

process
\textcircled{\small 1}ϒl$=\displaystyle\frac{180}{10}=18$\\
\textcircled{\small 2}1lʐ$=10$\\
\textcircled{\small 3}li2lʐj$=\displaystyle\frac{14+20}{2}=17$\\
\textcircled{\small 4}3lʐ$=28$\\
\textcircled{\small 5}͈́iWj$=iőlj-iŏlj=30-4=26$\\
\textcircled{\small 6}lʔ͈$=i3lʐj-i1lʐj=28-10=18$

{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
 ϒl & 1 &  l & 3      & ͈ & l \\ 
  @    &  lʐ &   & lʐ &  @@&  ͈ \\ \hline
        &        &           &          &      &       \\
   18 & 10   & 17      & 28     & 26 & 18   \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic102p.tex}
\end{center}

̃f[^́CCI̍ŋ10̃oXPbg{[̎ŋ_Ⴂɕׂ̂łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  &  &  &  &   \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10  \\ \hline
 _ & $12$ & $14$ & $14$ & $16$ & $16$ & $20$ & $20$ & $22$ & $22$ & $24$\\
\hline
\end{tabular}\end{center}\end{table}
}
 \\̃f[^ɂāC̒lꂼꋁ߁CЂ}Biϒl$+$ŋLj\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
 ϒl & 1 & l  & 3      & ͈ & l \\ 
  @    &  lʐ@&   & lʐ &  @@&  ͈ \\ \hline
        &        &           &          &      &       \\
        &        &           &          &      &       \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic103.tex}
\end{center}

process
\textcircled{\small 1}ϒl$=\displaystyle\frac{180}{10}=18$\\
\textcircled{\small 2}1lʐ$=14$\\
\textcircled{\small 3}li2lʐj$=\displaystyle\frac{16+20}{2}=18$\\
\textcircled{\small 4}3lʐ$=22$\\
\textcircled{\small 5}͈́iWj$=iőlj-iŏlj=24-12=12$\\
\textcircled{\small 6}lʔ͈$=i3lʐj-i1lʐj=22-14=8$

{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
 ϒl & 1 & l  & 3      & ͈ & l \\ 
  @    &  lʐ@&   & lʐ &  @@&  ͈ \\ \hline
        &        &           &          &      &       \\
   18 & 14   & 18      & 22     & 12 & 8   \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic103p.tex}
\end{center}

ssɂŇƂ̍ŒC̕ςƂƂC
̃f[^ꂽBf[^͏ʂľܓ̂ƂB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
  & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline
 C& $-12$ & $-9$ & $-3$ & $3$ & $10$ & $17$ \\ \hline \hline
  & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline
 C & $20$ & $19$ & $15$ & $7$ & $1$ & $-8$\\
\hline
\end{tabular}\end{center}\end{table}\\
̕\f[^̂тƁĈ悤łB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 f[^ԍ & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline
 C& $-12$ & $-9$ & $-8$ & $-3$ & $1$ & $3$ \\ \hline \hline
 f[^ԍ & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline
 C& $7$ & $10$ & $15$ & $17$ & $19$ & $20$\\
\hline
\end{tabular}\end{center}\end{table}
 \\i1j̃f[^̕ϒlC1lʐClC3lʐ߂B\\
i2jlʔ͈͂Ǝlʕ΍߂B\\
i3j̃f[^Ђ}̐}ɕ\ȂB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic108.tex}
\end{center}

process
i1jϒl$=\displaystyle\frac{60}{12}=5$\\
1lʐ$=\displaystyle\frac{-8-3}{2}=-5.5$\\
l$=\displaystyle\frac{3+7}{2}=5$\\
3lʐ$=\displaystyle\frac{15+17}{2}=16$\\
i2jlʔ͈$=16.0-(-5.5)=21.5$\\
lʕ΍$=\displaystyle\frac{21.5}{2}=10.75$

i1jϒl$=5$C1l$=-5.5$Cl$=5$C3lʐ$=16$C\\
i2jlʔ͈$=21.5$Clʕ΍$=10.75$\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic108p.tex}
\end{center}

17lŃeXgāC_̂悤łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
 \hline
  f[^ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\ \hline
  _i_j & 1 & 1 & 2 & 3 & 3 & 3 & 3 & 3 & 4 \\ \hline \hline
  f[^ԍ & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & ^\\ \hline
  _i_j & 4  & 4  & 6  & 7  & 7  & 8  & 8 &  10  & ^ \\ \hline
\end{tabular}\end{center}\end{table}}\\
i1jlʐ$Q_1,\,Q_2,\,Q_3$߂B\\
i2jlʔ͈͂߂B\\
i3jЂ}Biϒl͋LȂĂ悢j\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic109.tex}
\end{center}

process
i1j$Q_1=\displaystyle\frac{3+3}{2}=3,\,
Q_2=4,\,Q_3=\displaystyle\frac{7+7}{2}=7$\\
i2jlʔ͈$=7-3=4$\\

i1j$Q_1=3,\,Q_2=4,\,Q_3=7$Ci2j4C\\
i3j\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic109p.tex}
\end{center}

̃f[^́CRrjGXXgAɂ鏤iAƏiB
10Ԃ̔̔łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
 \hline
  f[^ԍ  & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline
  iAij & 8 & 4 & 13 & 9 & 21 & 5 & 16 & 23 & 11 & 17 \\ \hline \hline
  f[^ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline
  iBij & 21 & 11 & 7 & 24 & 14 & 9 & 15 & 17 & 25 & 22  \\ \hline
\end{tabular}\end{center}\end{table}}\\
lႢ̂̏ɕёւƁĈ悤łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
 \hline
  f[^ԍ  & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline
  iAij & 4 & 5 & 8 & 9 & 11 & 13 & 16 & 17 & 21 & 23 \\ \hline \hline
  f[^ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline
  iBij & 7 & 9 & 11 & 14 & 15 & 17 & 21 & 22 & 24 & 25  \\ \hline
\end{tabular}\end{center}\end{table}}\\
iAƏiB̃f[^̔Ђ}Biϒl͋LȂĂ悢j\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic110.tex}
\end{center}

process
iiAjF\\
$Q_1=8$C$Q_2=\displaystyle\frac{11+13}{2}=12$C$Q_3=17$C\\
iiBjF\\
$Q_1=11$C$Q_2=\displaystyle\frac{15+17}{2}=16$C$Q_3=22$

\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic110p.tex}
\end{center}

A$\sim$D̂ꂼ̃qXgOɂāC
f[^gĕ\Ђ}A$\sim$G̒IׁB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic115.tex}
\end{center}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic115p.tex}
\end{center}

process
Ⴆ΁C
A:\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccccccccc|}
\hline
 1 & 2 & 2 & 3 & 3 & 3 & 4 & 4 & 4 & 4 & 5 & 5 & 5 \\
 5 & 5 & 6 & 6 & 6 & 6 & 6 & 6 & 7 & 7 & 7 & 7 & 7 \\
\hline
\end{tabular}\end{center}\end{table}}\\
̏ꍇ$Q_1=3.5,\,Q_2=5,\,Q_3=6$\\
Ⴆ΁C
B:\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccccccccc|}
\hline
 1 & 1 & 2 & 2 & 2 & 3 & 3 & 3 & 3 & 4 & 4 & 4 & 4 \\
 4 & 4 & 4 & 4 & 5 & 5 & 5 & 5 & 6 & 6 & 6 & 7 & 7 \\
\hline
\end{tabular}\end{center}\end{table}}\\
̏ꍇ$Q_1=3,\,Q_2=5,\,Q_3=5$\\
Ⴆ΁C
C:\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccccccccc|}
\hline
 1 & 1 & 1 & 1 & 1 & 2 & 2 & 2 & 2 & 2 & 2 & 3 & 3 \\
 3 & 3 & 3 & 4 & 4 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 7 \\
\hline
\end{tabular}\end{center}\end{table}}\\
̏ꍇ$Q_1=2,\,Q_2=3,\,Q_3=4.5$\\
Ⴆ΁C
D:\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccccccccc|}
\hline
 1 & 1 & 1 & 1 & 1 & 2 & 2 & 2 & 2 & 3 & 3 & 3 & 4 \\
 4 & 5 & 5 & 5 & 6 & 6 & 6 & 6 & 7 & 7 & 7 & 7 & 7 \\
\hline
\end{tabular}\end{center}\end{table}}\\
̏ꍇ$Q_1=2,\,Q_2=4,\,Q_3=6$\\

A:C,\,B:E,\,C:A,\,D:G

A$\sim$D̂ꂼ̔Ђ}ɂāC
f[^gĕ\qXgOA$\sim$G̒IׁB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic116.tex}
\end{center}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic116p.tex}
\end{center}

process
Ⴆ΁C
A:\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccccccccc|}
\hline
 1 & 1 & 1 & 1 & 1 & 2 & 2 & 3 & 3 & 4 & 4 & 5 & 5 \\
 5 & 6 & 6 & 6 & 6 & 6 & 7 & 7 & 7 & 7 & 7 & 7 & 7 \\
\hline
\end{tabular}\end{center}\end{table}}\\
̏ꍇ$Q_1=2,\,Q_2=5,\,Q_3=7$\\
Ⴆ΁C
B:\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccccccccc|}
\hline
 1 & 1 & 2 & 2 & 3 & 3 & 4 & 4 & 4 & 4 & 5 & 5 & 5 \\
 5 & 6 & 6 & 6 & 6 & 6 & 6 & 7 & 7 & 7 & 7 & 7 & 7 \\
\hline
\end{tabular}\end{center}\end{table}}\\
̏ꍇ$Q_1=3.5,\,Q_2=5,\,Q_3=6.5$\\
Ⴆ΁C
C:\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccccccccc|}
\hline
 1 & 1 & 2 & 2 & 2 & 2 & 3 & 3 & 3 & 3 & 3 & 3 & 4 \\
 4 & 5 & 5 & 5 & 5 & 5 & 5 & 6 & 6 & 6 & 6 & 7 & 7 \\
\hline
\end{tabular}\end{center}\end{table}}\\
̏ꍇ$Q_1=2.5,\,Q_2=4,\,Q_3=5.5$\\
Ⴆ΁C
D:\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccccccccc|}
\hline
 1 & 1 & 1 & 2 & 2 & 2 & 2 & 2 & 3 & 3 & 3 & 4 & 4 \\
 4 & 4 & 5 & 5 & 5 & 6 & 6 & 6 & 6 & 6 & 7 & 7 & 7 \\
\hline
\end{tabular}\end{center}\end{table}}\\
̏ꍇ$Q_1=2,\,Q_2=4,\,Q_3=6$

A:A,\,B:G,\,C:C,\,D:E

̃f[^́CAZBZ9l̃nh{[̋L^ɕׂ̂łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
 \hline
  f[^ԍ  & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
  AZimj & 24 & 26 & 27 & 29 & 31 & 33 & 34 & 35 & 37 \\ \hline \hline
  f[^ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
  BZimj & 21 & 26 & 27 & 28 & 29 & 33 & 34 & 38 & 40  \\ \hline
\end{tabular}\end{center}\end{table}}\\
AZBZ̃f[^̔Ђ}Biϒl͋LȂĂ悢j\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic118.tex}
\end{center}

process
iiAjF\\
$Q_1=26.5$C$Q_2=31$C$Q_3=34.5$C\\
iiBjF\\
$Q_1=26.5$C$Q_2=29$C$Q_3=36$

\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic118p.tex}
\end{center}

̃f[^́C_앨10̏digjႢɕׂ̂łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  &  &  &  &   \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10  \\ \hline
 _ & $14$ & $15$ & $16$ & $19$ & $25$ & $27$ & $28$ & $28$ & $32$ & $36$\\
\hline
\end{tabular}\end{center}\end{table}}
 \\̃f[^ɂāC̒lꂼꋁ߁CЂ}Biϒl͋LȂĂ悢j\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
  1 & l & 3      & ͈ & l \\ 
  lʐ &     & lʐ &  @@&  ͈ \\ \hline
                &           &          &      &       \\
                &           &          &      &       \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic123.tex}
\end{center}

process
\textcircled{\small 1}1lʐ$=16$\\
\textcircled{\small 2}li2lʐj$=\displaystyle\frac{25+27}{2}=26$\\
\textcircled{\small 3}3lʐ$=28$\\
\textcircled{\small 4}͈́iWj$=iőlj-iŏlj=36-14=22$\\
\textcircled{\small 5}lʔ͈$=i3lʐj-i1lʐj=28-16=12$

{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
  1 & l & 3      & ͈ & l \\ 
  lʐ &   & lʐ &  @@&  ͈ \\ \hline
  &           &          &      &       \\
  16   & 26      & 28     & 22 & 12   \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic123p.tex}
\end{center}

̃f[^́C10l̐k̏eXg̓_Ⴂɕׂ̂łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  &  &  &  &   \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10  \\ \hline
 _ & $8$ & $8$ & $9$ & $9$ & $12$ & $12$ & $13$ & $13$ & $21$ & $22$\\
\hline
\end{tabular}\end{center}\end{table}}
 \\̃f[^ɂāC̒lꂼꋁ߁CЂ}Biϒl͋LȂĂ悢j\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 1    & l & 3      & ͈ & l \\ 
 lʐ &     & lʐ &  @@&  ͈ \\ \hline
 &           &          &      &       \\
 &           &          &      &       \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic125.tex}
\end{center}

process
\textcircled{\small 5}͈́iWj$=iőlj-iŏlj=22-8=14$\\
\textcircled{\small 6}lʔ͈$=i3lʐj-i1lʐj=13-9=4$

{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 1    & l & 3      & ͈ & l \\ 
 lʐ &     & lʐ &  @@&  ͈ \\ \hline
 &           &          &      &       \\
 9&     12      &    13      &   14   &   4    \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic125p.tex}
\end{center}

̃f[^́C10l̐k̏eXg̓_Ⴂɕׂ̂łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  &  &  &  &   \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10  \\ \hline
 _ & $9$ & $15$ & $17$ & $17$ & $18$ & $18$ & $20$ & $20$ & $22$ & $24$\\
\hline
\end{tabular}\end{center}\end{table}}
 \\̃f[^ɂāC̒lꂼꋁ߁CЂ}Biϒl͋LȂĂ悢j\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 1    & l & 3      & ͈ & l \\ 
 lʐ &     & lʐ &  @@&  ͈ \\ \hline
 &           &          &      &       \\
 &           &          &      &       \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic124.tex}
\end{center}

process
\textcircled{\small 5}͈́iWj$=iőlj-iŏlj=24-9=15$\\
\textcircled{\small 6}lʔ͈$=i3lʐj-i1lʐj=20-17=3$

{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 1    & l & 3      & ͈ & l \\ 
 lʐ &     & lʐ &  @@&  ͈ \\ \hline
 &           &          &      &       \\
 17&     18      &    20      &   15   &   3    \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic124p.tex}
\end{center}

̃f[^́CXɂ鏤iA10Ԃ̔̔𐔂̒Ⴂɕׂ̂łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  &  &  &  &   \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10  \\ \hline
 _ & $0$ & $1$ & $1$ & $2$ & $2$ & $2$ & $3$ & $4$ & $5$ & $7$\\
\hline
\end{tabular}\end{center}\end{table}}
 \\̃f[^ɂāC̒lꂼꋁ߁CЂ}Biϒl͋LȂĂ悢j\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 1    & l & 3      & ͈ & l \\ 
 lʐ &     & lʐ &  @@&  ͈ \\ \hline
 &           &          &      &       \\
 &           &          &      &       \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic126.tex}
\end{center}

process
\textcircled{\small 5}͈́iWj$=iőlj-iŏlj=7-0=7$\\
\textcircled{\small 6}lʔ͈$=i3lʐj-i1lʐj=4-1=3$

{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 1    & l & 3      & ͈ & l \\ 
 lʐ &     & lʐ &  @@&  ͈ \\ \hline
 &           &          &      &       \\
 1 &     2      &    4      &   7   &   3    \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic126p.tex}
\end{center}

̃f[^́CXɂ鏤iB10Ԃ̔̔𐔂̒Ⴂɕׂ̂łB\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  &  &  &  &   \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10  \\ \hline
 _ & $0$ & $1$ & $2$ & $2$ & $3$ & $4$ & $5$ & $6$ & $8$ & $10$\\
\hline
\end{tabular}\end{center}\end{table}}
 \\̃f[^ɂāC̒lꂼꋁ߁CЂ}Biϒl͋LȂĂ悢j\\
{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 1    & l & 3      & ͈ & l \\ 
 lʐ &     & lʐ &  @@&  ͈ \\ \hline
 &           &          &      &       \\
 &           &          &      &       \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic127.tex}
\end{center}

process
\textcircled{\small 5}͈́iWj$=iőlj-iŏlj=10-0=10$\\
\textcircled{\small 6}lʔ͈$=i3lʐj-i1lʐj=6-2=4$

{\scriptsize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 1    & l & 3      & ͈ & l \\ 
 lʐ &     & lʐ &  @@&  ͈ \\ \hline
 &           &          &      &       \\
 2 &     3.5      &    6      &   10   &   4    \\
\hline
\end{tabular}\end{center}\end{table}}
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic127p.tex}
\end{center}

\hspace{8pt} ̔Ђ}ɂāCΉqXgOIтȂB\\
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/pic1362.eps}
 \end{center}\end{figure} 
 \begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|} \hline
  (1) & \hspace{30pt} & (2) & \hspace{30pt} & (3) & \hspace{30pt}  \\ \hline
\end{tabular}\end{center}\end{table}

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|} \hline
  (1) & \textcircled{\small 3} & (2) & \textcircled{\small 2} & (3) & \textcircled{\small 1}  \\ \hline
\end{tabular}\end{center}\end{table}

̃f[^́CAЂ10X܂ɂnCubhԂ̌Ԕグ䐔łB\\
\hspace{12pt}$12,\,10,\,15,\,10,\,13,\,8,\,11,\,18,\,11,\,11$ij\\
\hspace{8pt} ̃f[^̔Ђ}ƂčłK؂Ȃ̂\fbox{\,C\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2601m0601.eps}
 \end{center}\end{figure} 

process
ɕтƁC\\
$8,\,10,\,10,\,11,\,11,\,11,\,12,\,13,\,15,\,18$\\
$Q_1=10,Q_2=11,Q_3=13$

\textcircled{\small 2}

}́C2̖싅`[ACB10̓_ꂼꔠЂ}ɕ\̂łB
́iajCibjCicj̋Lq̐ɂāCK؂Ȃ̂\fbox{\,C\,}łB\\
\begin{table}[!htb]
  \begin{center}\begin{tabular}{|c l|} \hline
iaj& `[A̓_̍őĺC`[B \\
      & ̓_̍ől傫B\\ 
ibj& `[A̓_͈̔͂́C`[B \\
      & _͈̔͂傫B\\
icj& `[A̓_̎lʔ͈͂́C`[\\
      & B̓_̎lʔ͈͂ƓB\\ \hline
  \end{tabular}\end{center}
 \hspace{8pt} \textcircled{\small 1}$\sim $\textcircled{\small 4}̂IׁB\\
 \textcircled{\small 1}\,iajCibjCicj̋Lq̂1͐C2͌ĂB\\
  \textcircled{\small 2}\,iajCibjCicj̋Lq̂2͐C1͌ĂB\\
   \textcircled{\small 3}\,iajCibjCicj̋Lqׂ͂ĐB\\
    \textcircled{\small 4}\,iajCibjCicj̋Lqׂ͂ČĂB\\
\end{table} 
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=30mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2702m0601.eps}
 \end{center}\end{figure} 

\textcircled{\small 3}

̃f[^́Cn_ɂ鐳߂ߌ1܂ł̎Ԃ̒ʍsʂ9Ԓׂ̂łB\\
$29,\,17,\,22,\,12,\,15,\,31,\,35,\,26,\,20$ij\\
\hspace{8pt} ̃f[^ɂĂ̐ƂāC{\bf Ă}\fbox{\,A\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\textcircled{\small 1}\,ŏl12Cől35łB\\
\textcircled{\small 2}\,1lʐ16C3lʐ30łB\\
\textcircled{\small 3}\,l22łB\\
\textcircled{\small 4}\,ϒl22łB

process
ɕׂƁC\\
$12,\,15,\,17,\,20,\,22,\,26,\,29,\,31,\,35$ij\\
$Q_1=16,Q_2=22,Q_3=30$\\
@\\
̕ϒl20ƂƁC̕ϒl̂\\
$-8,\,-5,\,-3,\,0,\,+2,\,+6,\,+9,\,+11,\,+15$ij\\
āCϒl$20+\displaystyle\frac{27}{9}=23.0$

\textcircled{\small 4}

20l̐kC10__̃eXgsʂ_̏ɕׂƎ̂悤ɂȂB
̃f[^̔Ђ}\fbox{\,C\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB
\\
3,\,3,\,3,\,4,\,4,\,4,\,4,\,5,\,5,\,5,\,5,\,6,\,6,\,6,\,6,\,7,\,7,\,9,\,9,\,10i_j\\
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2602m0601.eps}
 \end{center}\end{figure} 

process
$3,\,3,\,3,\,4,\,4,\mid \,4,\,4,\,5,\,5,\,5,\mid \,5,\,6,\,6,\,6,\,6,\mid \,7,\,7,\,9,\,9,\,10$i_j\\
$Q_1=4$C$Q_2=5$C$Q_3=6.5$

\textcircled{\small 2}

̃f[^́C싅`[̃sb`[ƃLb`[7l̔NԂ̃z[̃f[^łB1lʐ$Q_1$C2lʐ$Q_2$C3lʐ$Q_3$߂B\\
\hspace{20pt} 4,\,1,\,0,\,2,\,5,\,7,\,9i{j

process
l̏ɕׂƁC\\
0,\,1,\,2,\,4,\,5,\,7,\,9

$Q_1=1$,\,$Q_2=4$,\,$Q_3=7$

\hspace{8pt} 
̐}́C鍂Z1N280lɍsmFeXg̓_̃f[^̔Ђ}łB\\
\hspace{8pt} 
̔Ђ}ǂݎ邱Ƃ\fbox{\bf\, E \,}łB\\
\hspace{8pt} \textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,30_̐k70lłB\\
\textcircled{\small 2}\,50_ȏ̐k210lȏアB\\
\textcircled{\small 3}\,60_̐k͔ȏアB\\
\textcircled{\small 4}\,ϓ_70_ȏłB\\
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=50mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2801m602.eps}
 \end{center}\end{figure} 

\textcircled{\small 3}

\hspace{8pt} 
̃f[^́CtbgTɎQ10`[ɏĂ
I̐lɕׂ̂łB\\
\hspace{20pt}$8,\,9,\,10,\,10,\,11,\,12,\,12,\,14,\,17,\,18$ilj\\
̃f[^̔Ђ}ƂĐ̂͂ǂꂩB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2901m601.eps}
 \end{center}\end{figure}

process
$Q_1=10,Q_2=11.5,Q_3=14$

\textcircled{\small 2}

\hspace{8pt} 
}́CAЁCBЂɂāCꂼ]ƈ50l̒ʋΎԂ̃f[^̔Ђ}łB\\
\hspace{8pt} 
̃f[^ɂĂ̋LqƂ{\bf K؂łȂ}\fbox{\bf\, C \,}łB\\
\hspace{8pt} \textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,AЂɂ͒ʋΎԂ50ȏ̐l25lȏアB\\
\textcircled{\small 2}\,ʋΎԂ70ȏ̐lAЂ̕B\\
\textcircled{\small 3}\,ʋΎԂ40ȉ̐lBЂ̕B\\
\textcircled{\small 4}\,AЁCBЂʂĒʋΎԂłZlAЂɂB
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=40mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2802m601.eps}
 \end{center}\end{figure} 

process
\textcircled{\small 1}\,AЂɂ͒ʋΎ50ȏオ26lB\\
\textcircled{\small 2}\,ʋΎ70ȏAЖ11lCB13lB\\
\textcircled{\small 3}\,ʋΎ40ȉAЖ11lCB14lB

\textcircled{\small 2}

X|[cNủ50lɑ΂āC1̉^Ԃ𒲍C
̃f[^𔠂Ђ}ɕ\B̌ʁC30ȏ^l25l葽C
lʔ͈͂30菬B
̃f[^̔Ђ}ƂāCłK؂Ȃ̂\fbox{\,\bf E\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2902m601.eps}
 \end{center}\end{figure} 

process
30ȏ^l25l葽C璆l30ȏB

\textcircled{\small 2}

}́C鍂Z1N203lɍspCC
w̃eXg̓_𔠂Ђ}ɕ\̂łB
Ŝ41ȏ̐k80_ȏłȂ(A)łB
܂C60_ȏ̍łȂ(B)łB
(A)C(B)ɂĂ͂܂̂̑g\fbox{\bf\hspace{8pt} C \hspace{8pt}}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂琳̂IׁB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
\hline
  & \textcircled{\small 1} & \textcircled{\small 2} & \textcircled{\small 3} & \textcircled{\small 4} \\
\hline
  (A) & p & w & w &  \\ \hline
  (B) & w &  & p & p \\ \hline
\end{tabular}\end{center}\end{table}
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=60mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h3001m10601.eps}
 \end{center}\end{figure} 

process
w$Q_3$80ȏBp$Q_2$
60ȏB

\textcircled{\small 3}

镔̕10NׂāC̃f[^jʂɔЂ}ɂ܂Ƃ߂B\\
̃f[^ɂĂ̋Lq̂CЂ}{\bf ǂݎȂ}Ƃ
\fbox{\bf\, C \,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂IׁB\\
\textcircled{\small 1}\,jq̑1lʐƑ3lʐ͓B\\
\textcircled{\small 2}\,jq3lɂȂ邱ƂȂB\\
\textcircled{\small 3}\,jq̕ϒlƏq̕ϒl͓B\\
\textcircled{\small 4}\,f[^͈݂̔͂ƁC
jq菗q̕U΂傫B
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=60mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h3101602.eps}
 \end{center}\end{figure} 

\textcircled{\small 3}

̃f[^́Cw10lɁCĂC̐𕷂̂łB\\
\hspace{10pt} $5,\,8,\,5,\,9,\,8,\,10,\,3,\,6,\,4$\\
̃f[^̔Ђ}ƂĐ̂\fbox{\bf\, I \,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h3002m601.eps}
 \end{center}\end{figure} 

process
ɕׂƁC\\
$3,\,4,\,5,\,5,\,6,\,6,\,8,\,8,\,9,\,10$\\
$Q_1=5,Q_2=6,\,Q_3=8$

\textcircled{\small 4}








[Level6]
UƕW΍
̃f[^́C5̒Ŋϑꂽ錎̍~JłB\\
\hspace{20pt} 8,\,9,\,9,\,11,\,13ij\\
\hspace{8pt} ̃f[^̕ϒl10ijłB
̃f[^̕W΍̌vZ\fbox{\,E\,}łB\\
\hspace{8pt} \textcircled{\small 1}$\sim$\textcircled{\small 4}
̂琳̂IׁB\\
\textcircled{\small 1}\,
\footnotesize
$\sqrt{\displaystyle\frac{ |8-10|+|9-10|+|9-10|+|11-10|+|13-10|}{5}}$
\normalsize
\\
\textcircled{\small 2}\,
\footnotesize
$\sqrt{\displaystyle\frac{(8-10)^2+(9-10)^2+(9-10)^2+(11-10)^2+(13-10)^2}{5}}$
\normalsize
\\\textcircled{\small 3}\,
\footnotesize
$\displaystyle\frac{ |8-10|+|9-10|+|9-10|+|11-10|+|13-10|}{5}$
\normalsize
\\
\textcircled{\small 4}\,
\footnotesize
$\displaystyle\frac{(8-10)^2+(9-10)^2+(9-10)^2+(11-10)^2+(13-10)^2}{5}$\normalsize

\textcircled{\small 2}

NX5l̏eXg̓_͎̒ʂłB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 _ & $4$ & $6$ & $8$ & $5$ & $7$\\ \hline
 ΍ &  &  &  &  & \\ \hline
 $΍^2$ &  &  &  &  & \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1jϒl$\overline x$߂B\\
i2j̕\̋󗓂𖄂߁CU$s^2$߂B\\
i3jW΍$s$߂BC$\sqrt{2}=1.41$ƂB

process
i1j$\overline x=\displaystyle\frac{30}{5}=6$\\
i2j\\
U$s^2=\displaystyle\frac{4+0+4+1+1}{5}\\
=\displaystyle\frac{10}{5}=2$\\
i3jW΍$s=\sqrt{2}=1.41$

{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 _ & $4$ & $6$ & $8$ & $5$ & $7$\\ \hline
 ΍ & $-2$ & $0$ & $2$ & $-1$  & $1$ \\ \hline
 $΍^2$ & 4 & 0 & 4 & 1 & 1 \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1j6Ci2j2Ci3j$1.41$

NX5l̏eXg̓_͎̒ʂłB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 _ & $6$ & $3$ & $7$ & $10$ & $9$\\ \hline
 ΍ &  &  &  &  & \\ \hline
 $΍^2$ &  &  &  &  & \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1jϒl$\overline x$߂B\\
i2j̕\̋󗓂𖄂߁CU$s^2$߂B\\
i3jW΍$s$߂BC$\sqrt{2}=1.41$C$\sqrt{3}=1.73$C$\sqrt{6}=2.45$ƂB

process
i1j$\overline x=\displaystyle\frac{35}{5}=7$\\
i2j\\
U$s^2=\displaystyle\frac{1+16+0+9+4}{5}\\
=\displaystyle\frac{30}{5}=6$\\
i3jW΍$s=\sqrt{6}=2.45$

{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 _ & $6$ & $3$ & $7$ & $10$ & $9$\\ \hline
 ΍ & $-1$ & $-4$ & $0$ & $3$  & $2$ \\ \hline
 $΍^2$ & 1 & 16 & 0 & 9 & 4 \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1j7Ci2j6Ci3j$2.45$

̕\5l̑̏d𒲂ׂ̂łB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 ̏d(kg) & $48$ & $54$ & $50$ & $56$ & $52$\\ \hline
 ΍ &  &  &  &  & \\ \hline
 $΍^2$ &  &  &  &  & \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1jϒl$\overline x$߂B\\
i2j̕\̋󗓂𖄂߁CU$s^2$߂B\\
i3jW΍$s$߂BC$\sqrt{2}=1.41$ƂB

process
i1j$\overline x=\displaystyle\frac{260}{5}=52$\\
i2j\\
U$s^2=\displaystyle\frac{16+4+4+16+0}{5}\\
=\displaystyle\frac{40}{5}=8$\\
i3jW΍$s=\sqrt{8}=2\times \sqrt{2}=2\times 1.41=2.82$

{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 ̏d(kg) & $48$ & $54$ & $50$ & $56$ & $52$\\ \hline
 ΍ & $-4$ & $2$ & $-2$ & $4$  & $0$ \\ \hline
 $΍^2$ & 16 & 4 & 4 & 16 & 0 \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1j52Ci2j8Ci3j$2.82$

̕\6l̐g𒲂ׂʂłB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  & \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline
 g(cm) & $142$ & $158$ & $146$ & $148$ & $154$ & $152$\\ \hline
 ΍ &  &  &  &  & & \\ \hline
 $΍^2$ &  &  &  &  & & \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1jϒl$\overline x$߂B\\
i2j̕\̋󗓂𖄂߁CU$s^2$߂B\\
i3jW΍$s$߂BC$\sqrt{7}=2.65$ƂB

process
i1j$\overline x=\displaystyle\frac{900}{6}=150$\\
i2j\\
U$s^2=\displaystyle\frac{64+64+16+4+16+4}{6}\\
=\displaystyle\frac{168}{6}=28$\\
i3jW΍$s=\sqrt{28}=2\times \sqrt{7}=2\times 2.65=5.30$

{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  & \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline
 g(cm) & $142$ & $158$ & $146$ & $148$ & $154$ & $152$\\ \hline
 ΍ & $-8$ & $8$ & $-4$ & $-2$ & $4$ & $2$ \\ \hline
 $΍^2$ & 64 & 64 & 16 & 4 & 16 & 4\\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1j150Ci2j28Ci3j$5.30$

̕\́C鍂Z̃oXPbg{[A̍ŋ6ɂ鐬V[g̖{łB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6  \\ \hline
 _ & $9$ & $7$ & $8$ & $7$ & $8$ & $9$\\ \hline
 ΍ &  &  &  &  &  & \\ \hline
 $΍^2$ &  &  &  &  &  & \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1jV[g̖{̕ϒl߂B\\
i2j̕\̋󗓂𖄂߂B\\
i3jU𕪐̌`œB\\
i4jW΍2ʂ܂ŋ߂BC$\sqrt{6}=2.45$ƂB

process
i1jϒl$=\displaystyle\frac{48}{6}=8{$\\
i2j\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6  \\ \hline
 _ & $9$ & $7$ & $8$ & $7$ & $8$ & $9$\\ \hline
 ΍ & $1$ & $-1$ & $0$ & $-1$ & $0$ & $-1$\\ \hline
 $΍^2$ & 1 & 1 & 0 & 1 & 0 & 1 \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i3j$s^2=\displaystyle\frac{4}{6}=\displaystyle\frac{2}{3}$\\
i4j$s=\sqrt{\displaystyle\frac{2}{3}}=\displaystyle\frac{\sqrt{6}}{3}=\displaystyle\frac{2.45}{3}=0.816\cdots\\
\fallingdotseq 0.82$

i1j8{Ci2jLCi3j$\displaystyle\frac{2}{3}$Ci4j$0.82$

̕\́C鍂Z̃oXPbg{[B̍ŋ6ɂ鐬V[g̖{łB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6  \\ \hline
 _ & $2$ & $9$ & $12$ & $3$ & $10$ & $12$\\ \hline
 ΍ &  &  &  &  &  & \\ \hline
 $΍^2$ &  &  &  &  &  & \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1jV[g̖{̕ϒl߂B\\
i2j̕\̋󗓂𖄂߂B\\
i3jU𕪐̌`œB\\
i4jW΍2ʂ܂ŋ߂BC$\sqrt{3}=1.73$ƂB

process
i1jϒl$=\displaystyle\frac{48}{6}=8{$\\
i2j\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5 & 6  \\ \hline
 _ & $2$ & $9$ & $12$ & $3$ & $10$ & $12$\\ \hline
 ΍ & $-6$ & $1$ & $4$ & $-5$ & $2$ & $4$\\ \hline
 $΍^2$ & 36 & 1 & 16 & 25 & 4 & 16 \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i3j$s^2=\displaystyle\frac{36+1+16+25+4+16}{6}\\
=\displaystyle\frac{98}{6}=\displaystyle\frac{49}{3}$\\
i4j$s=\sqrt{\displaystyle\frac{49}{3}}=\displaystyle\frac{7}{\sqrt{3}}=\displaystyle\frac{7\sqrt{3}}{3}\\
=\displaystyle\frac{7\times 1.73}{3}=4.036\cdots\fallingdotseq 4.04$

i1j8{Ci2jLCi3j$\displaystyle\frac{49}{3}$Ci4j$4.04$

̃f[^ɂāCϒl$\overline x$ƕU$s^2$߂B
C$s^2$ɂĂ\\
$s^2=\displaystyle\frac{1}{n}\{ (x_1-\overline x)^2+ (x_2-\overline x)^2+\cdots+(x_n-\overline x)^2\}$\\
𗘗p邱ƁB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
$1$ & $1$ & $3$ & $5$ & $5$ \\
\hline
\end{tabular}\end{center}\end{table}

process
$\overline x=\displaystyle\frac{15}{5}=3$\\
$s^2=\displaystyle\frac{1}{5}\{ (-2)^2+(-2)^2+0^2+2^2+2^2 \}
=\displaystyle \frac{16}{5}\\
=3.2$

$\overline x=3,\,s^2=3.2$

̃f[^ɂāCϒl$\overline x$ƕU$s^2$߂B
C$s^2$ɂĂ\\
$s^2=\displaystyle\frac{1}{n}\{ (x_1-\overline x)^2+ (x_2-\overline x)^2+\cdots+(x_n-\overline x)^2\}$\\
𗘗p邱ƁB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 $2$ & $3$ & $3$ & $3$ & $4$ \\
\hline
\end{tabular}\end{center}\end{table}

process
$\overline x=\displaystyle\frac{15}{5}=3$\\
$s^2=\displaystyle\frac{1}{5}\{ (-1)^2+0^2+0^2+0^2+1^2 \}
=\displaystyle \frac{2}{5}\\
=0.4$

$\overline x=3,\,s^2=0.4$

̃f[^ɂāCϒl$\overline x$ƕU$s^2$߂B
C$s^2$ɂĂ\\
$s^2=\displaystyle\frac{1}{n}\{ (x_1-\overline x)^2+ (x_2-\overline x)^2+\cdots+(x_n-\overline x)^2\}$\\
𗘗p邱ƁB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 $4$ & $6$ & $8$ & $5$ & $7$ \\
\hline
\end{tabular}\end{center}\end{table}

process
$\overline x=\displaystyle\frac{30}{5}=6$\\
$s^2=\displaystyle\frac{1}{5}\{ (-2)^2+0^2+2^2+(-1)^2+1^2 \}=2$

$\overline x=6,\,s^2=2$

̃f[^ɂāCϒl$\overline x$ƕU$s^2$߂B
C$s^2$ɂĂ\\
$s^2=\displaystyle\frac{1}{n}\{ (x_1-\overline x)^2+ (x_2-\overline x)^2+\cdots+(x_n-\overline x)^2\}$\\
𗘗p邱ƁB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccccc|}
\hline
 $4$ & $4$ & $4$ & $4$ & $5$ & $5$ & $7$ & $7$\\
\hline
\end{tabular}\end{center}\end{table}

process
ϒl$\overline x=\displaystyle\frac{40}{8}=5$\\
U$s^2=\displaystyle\frac{(-1)^2\times 4+0^2\times 2+2^2\times 2}{8}\\
=\displaystyle\frac{12}{8}=\displaystyle\frac{3}{2}=1.5$\\

$\overline x=5,\,s^2=1.5$

̃f[^ɂāCϒl$\overline x$ƕU$s^2$߂B
C$s^2$ɂĂ\\
$s^2=\displaystyle\frac{1}{n}\{ (x_1-\overline x)^2+ (x_2-\overline x)^2+\cdots+(x_n-\overline x)^2\}$\\
𗘗p邱ƁB
i2񏈗ZpҎj\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 $3$ & $2$ & $7$ & $7$ & $6$ \\
\hline
\end{tabular}\end{center}\end{table}

process
$\overline x=\displaystyle\frac{25}{5}=5$\\
$s^2=\displaystyle\frac{1}{5}\{ (-2)^2+(-3)^2+2^2+2^2+1^2 \}=\displaystyle\frac{22}{5}=4.4$

$\overline x=5,\,s^2=4.4$

鐶k̐w̃eXgi100__jɂāC
7񕪂̓_𒲂ׂƂ뎟̂悤łB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccc|}
\hline
 $70$ & $85$ & $65$ & $95$ & $100$ & $85$ & $60$ \\
\hline
\end{tabular}\end{center}\end{table}\\
i1j_̕ϒl$\overline x$߂B\\
i2j̕\CU$s^2$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccc|}
\hline
 $x$             & $70$ & $85$ & $65$ & $95$ & $100$ & $85$ & $60$ \\ \hline
 $x-\overline x$ &  &  &  &  &  &  &  \\ \hline
 $(x-\overline x)^2$ &  &  &  &  &  &  &  \\
\hline
\end{tabular}\end{center}\end{table}\\
i3jW΍$s$߂BC$\sqrt{2}=1.41$ƂB

process
l85̕ϒlƂƁC\\
ϒl$=85+\displaystyle\frac{-15+0-20+10+15+0-25}{7}\\
=85-\displaystyle\frac{35}{7}=85-5=80$\\
U$s^2=\displaystyle\frac{1400}{7}=200$\\
W΍$s=\sqrt{200}=\sqrt{2} \times 10=1.41 \times 10=14.1$

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccc|}
\hline
 $x$             & $70$ & $85$ & $65$ & $95$ & $100$ & $85$ & $60$ \\ \hline
 $x-\overline x$ & $-10$ & $5$ & $-15$ & $15$ & $20$ & $5$ & $-20$ \\ \hline
 $(x-\overline x)^2$ & $100$ & $25$ & $225$ & $225$ & $400$ & $25$ & $400$ \\
\hline
\end{tabular}\end{center}\end{table}
i1jϒl$=80$Ci2jU$=200$Ci3jW΍$=14.1$

̃f[^ɂĎ̖₢ɓB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccccc|}
\hline
 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
\end{tabular}\end{center}\end{table}\\
i1jf[^̕ϒl$\overline x$߂B\\
i2j̕\CU$s^2$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccc|}
\hline
 $x$             & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
 $x-\overline x$     &  &  &  &  &  &  & \\ \hline
 $(x-\overline x)^2$ &  &  &  &  &  &  &  \\
\hline
\end{tabular}\end{center}\end{table}\\
i3jW΍$s$߂B

process
i1j$\overline x=\displaystyle\frac{42}{7}=6$\\
i2j\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccccc|}
\hline
 $x$             & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
 $x-\overline x$ & $-3$ & $-2$ & $-1$ & 0 & 1 & 2 & 3 \\ \hline
 $(x-\overline x)^2$ & 9 & 4 & 1 & 0 & 1 & 4 & 9 \\
\hline
\end{tabular}\end{center}\end{table}\\
U$s^2=\displaystyle\frac{28}{7}=4$\\
i3jW΍$s=2$

i1j6Ci2j4Ci3j2

̃f[^ɂĎ̖₢ɓB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 3 & 5 & 6 & 7 & 9 \\
\hline
\end{tabular}\end{center}\end{table}\\
i1jf[^̕ϒl$\overline x$߂B\\
i2j̕\CU$s^2$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccc|}
\hline
 $x$             & 3 & 5 & 6 & 7 & 9 \\ \hline
 $x-\overline x$     &  &  &  &  &   \\ \hline
 $(x-\overline x)^2$ &  &  &  &  &   \\
\hline
\end{tabular}\end{center}\end{table}\\
i3jW΍$s$߂B

process
i1j$\overline x=\displaystyle\frac{30}{5}=6$\\
i2j\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccc|}
\hline
 $x$                 & 3 & 5 & 6 & 7 & 9 \\ \hline
 $x-\overline x$     & $-3$ & $-1$ & 0 & 1 & 3  \\ \hline
 $(x-\overline x)^2$ & 9 & 1 & 0 & 1 & 9  \\
\hline
\end{tabular}\end{center}\end{table}\\
U$s^2=\displaystyle\frac{20}{5}=4$\\
i3jW΍$s=\sqrt{4}=2$

i1j6Ci2j4Ci3j2

l50l̂g̐kɂăeXgʁĈ悤ȕ\𓾂B
\CW΍߂BC$\sqrt{2}=1.41$ƂB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
 \hline
  _ & l & v & ΍ & $΍^2$ & $΍^2$ \\
  i_j&ilj& _ &     &          & $\times l$\\ \hline
  1 & 4 &   &  &  & \\
  2 & 14 &   &  &  & \\ 
  3 & 16 &   &  &  & \\
  4 & 10 &   &  &  & \\
  5 & 6 &   &  &  & \\ \hline
  v & 50 &  & ^ & ^ & \\ \hline
  ^ & ϒl &  & ^ & U & \\ \hline
\end{tabular}\end{center}\end{table}

process
W΍$=\sqrt{1.28}=\sqrt{\displaystyle\frac{128}{100}}
=\displaystyle\frac{8\times \sqrt{2}}{10}\\
=\displaystyle\frac{8\times 1.41}{10}
=1.128$

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
 \hline
  _ & l & v & ΍ & $΍^2$ & $΍^2$ \\
  i_j&ilj& _ &     &          & $\times l$\\ \hline
  1 & 4 &  4 & $-2$ & 4 & 16 \\
  2 & 14 &  28 & $-1$ & 1 & 14\\ 
  3 & 16 &  48 & 0 & 0 & 0 \\
  4 & 10 &  40 & 1 & 1 & 10\\
  5 & 6 &  30 & 2 & 4 & 24\\ \hline
  v & 50 & 150 & ^ & ^ & 64 \\ \hline
  ^ & ϒl & 3 & ^ & U & 1.28 \\ \hline
\end{tabular}\end{center}\end{table}\\
W΍$=1.128$

̕\͂Wc30l̐g̓xz\łB
ϒlƕU߂B
CUɂĂ͂͏_ȉ1܂ŋ߂B\\
{\footnotesize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
 \hline
  K & l & Kl & ΍ & $΍^2$ & $΍^2$ \\
  icmj&ilj& (cm) &     &          & $\times l$\\ \hline
  140ȏ150 & 2 &   &  &  & \\
  150ȏ160 & 5 &   &  &  & \\ 
  160ȏ170 & 16 &   &  &  & \\
  170ȏ180 & 5 &   &  &  & \\
  180ȏ190 & 2 &   &  &  & \\ \hline
  v & 30 &  & ^ & ^ & \\ \hline
  ^ & ϒl &  & ^ & U & \\ \hline
\end{tabular}\end{center}\end{table}}

process
U$=\displaystyle\frac{2600}{30}
=86.6\cdots$

{\footnotesize
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
 \hline
  K & l & Kl & ΍ & $΍^2$ & $΍^2$ \\
  icmj&ilj& (cm) &     &          & $\times l$\\ \hline
  140ȏ150 & 2 &  145 & $-20$ & 400 & 800\\
  150ȏ160 & 5 &  155 & $-10$ & 100 & 500\\ 
  160ȏ170 & 16 &  165 & 0 & 0 & 0\\
  170ȏ180 & 5 &  175 & 10 & 100 & 500\\
  180ȏ190 & 2 & 185  & 20 & 400 & 800\\ \hline
  v & 30 & 4950 & ^ & ^ & 2600\\ \hline
  ^ & ϒl & 165 & ^ & U & 86.7\\ \hline
\end{tabular}\end{center}\end{table}}
 \\U$=86.7$

3{̃UCB̋x͎̒ʂłB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
\hline
 f[^ &  &  & \\
 ԍ & 1 & 2 & 3 \\ \hline
 x(kg) & $37$ & $43$ & $52$\\ \hline
 ΍ &  &  & \\ \hline
 $΍^2$ &  &  & \\ \hline
\end{tabular}\end{center}\end{table}} \\
i1jϒl$\overline x$߂B\\
i2j̕\̋󗓂𖄂߁CU$s^2$߂B

process
i1j$\overline x=\displaystyle\frac{132}{3}=44$\\
i2j\\
U$s^2=\displaystyle\frac{49+1+64}{3}\\
=\displaystyle\frac{114}{3}=38$\\

i1jϒl$=44$kgC\\
i2jU$=38$\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
\hline
 f[^ &  &  & \\
 ԍ & 1 & 2 & 3 \\ \hline
 x(kg) & $37$ & $43$ & $52$\\ \hline
 ΍ & $-7$ & $-1$ & $8$ \\ \hline
 $΍^2$ & 49 & 1 & 64\\ \hline
\end{tabular}\end{center}\end{table}}

①ɂ5oāC̏d͂Ă݂Ƃ뎟̕\̂悤łB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  & & &\\
 ԍ & 1 & 2 & 3 & 4 & 5\\ \hline
 ϗ(g) & $63$ & $65$ & $67$ & $70$ & $75$\\ \hline
 ΍ &  &  & & &\\ \hline
 $΍^2$ &  &  & & &\\ \hline
\end{tabular}\end{center}\end{table}} \\
i1jϒl$\overline x$߂B\\
i2j̕\̋󗓂𖄂߁CU$s^2$߂B

process
i1j$\overline x=\displaystyle\frac{340}{5}=68$\\
i2j\\
U$s^2=\displaystyle\frac{25+9+1+4+49}{5}\\
=\displaystyle\frac{88}{5}=17.6$\\

i1jϒl$=68$kgC\\
i2jU$=17.6$\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  & & &\\
 ԍ & 1 & 2 & 3 & 4 & 5\\ \hline
 ϗ(g) & $63$ & $65$ & $67$ & $70$ & $75$\\ \hline
 ΍ & $-5$ & $-3$ & $-1$ & $2$ & $7$\\ \hline
 $΍^2$ & 25 & 9 & 1 &4 & 49\\ \hline
\end{tabular}\end{center}\end{table}}

̃f[^ɂāCϒl$\overline x$ƕU$s^2$߂B
C$s^2$ɂĂ\\
$s^2=\displaystyle\frac{1}{n}\{ (x_1-\overline x)^2+ (x_2-\overline x)^2+\cdots+(x_n-\overline x)^2\}$\\
𗘗p邱ƁB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 $7$ & $5$ & $8$ & $6$ & $4$ \\
\hline
\end{tabular}\end{center}\end{table}

process
$\overline x=\displaystyle\frac{30}{5}=6$\\
$s^2=\displaystyle\frac{1}{5}\{ 1^2+(-1)^2+2^2+0^2+(-2)^2 \}
=\displaystyle \frac{10}{5}\\
=2$

$\overline x=6,\,s^2=2$

̃f[^ɂāCϒl$\overline x$ƕU$s^2$߂B
C$s^2$ɂĂ\\
$s^2=\displaystyle\frac{1}{n}\{ (x_1-\overline x)^2+ (x_2-\overline x)^2+\cdots+(x_n-\overline x)^2\}$\\
𗘗p邱ƁB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 $2$ & $7$ & $10$ & $5$ & $6$ \\
\hline
\end{tabular}\end{center}\end{table}

process
$\overline x=\displaystyle\frac{30}{5}=6$\\
$s^2=\displaystyle\frac{1}{5}\{ (-4)^2+1^2+4^2+(-1)^2+0^2 \}
=\displaystyle \frac{16+1+16+1+0}{5}=\displaystyle\frac{34}{5}\\
=6.8$

$\overline x=6,\,s^2=6.8$

̃f[^ɂāCϒl$\overline x$ƕU$s^2$߂B
C$s^2$ɂĂ\\
$s^2=\displaystyle\frac{1}{n}\{ (x_1-\overline x)^2+ (x_2-\overline x)^2+\cdots+(x_n-\overline x)^2\}$\\
𗘗p邱ƁB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|cccccc|}
\hline
 $3$ & $4$ & $6$ & $7$ & $9$ & $13$ \\
\hline
\end{tabular}\end{center}\end{table}

process
$\overline x=\displaystyle\frac{42}{6}=7$\\
$s^2=\displaystyle\frac{1}{6}\{ (-4)^2+(-3)^2+(-1)^2+0^2+2^2+6^2 \}
=\displaystyle \frac{16+9+1+0+4+36}{6}=\displaystyle\frac{66}{6}\\
=11$

$\overline x=7,\,s^2=11$

̃f[^́CoXPbg{[̑ITl̐głB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 173 & 176 & 180 & 182 & 184 \\
\hline
\end{tabular}\end{center}\end{table}\\
i1jf[^̕ϒl$\overline x$߂B\\
i2j̕\CU$s^2$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccc|}
\hline
 $x$                     & 173 & 176 & 180 & 182 & 184 \\ \hline
 $x-\overline x$     &  &  &  &  &  \\ \hline
 $(x-\overline x)^2$ &  &  &  &  &   \\
\hline
\end{tabular}\end{center}\end{table} \\
i3jW΍$s$߂B

process
i1j̕ϒl175ƂƁC$x-\overline x$̒l͏ɁC$-2,1,5,7,9$iv20jł邩C\\
$\overline x=175+\displaystyle\frac{20}{5}=175+4=179$\\
i2j\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccc|}
\hline
 $x$                     & 173 & 176 & 180 & 182 & 184 \\ \hline
 $x-\overline x$     & $-6$ & $-3$ & $1$ & 3 & 5 \\ \hline
 $(x-\overline x)^2$ & 36 & 9 & 1 & 9 & 25  \\
\hline
\end{tabular}\end{center}\end{table} \\
 U$s^2=\displaystyle\frac{80}{5}=16$\\
i3jW΍$s=4$

i1j179Ci2j16Ci3j4

̃f[^ɂĎ̖₢ɓB\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|ccccc|}
\hline
 1 & 4 & 5 & 13 & 17 \\
\hline
\end{tabular}\end{center}\end{table}\\
i1jf[^̕ϒl$\overline x$߂B\\
i2j̕\CU$s^2$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccc|}
\hline
 $x$                     & 1 & 4 & 5 & 13 & 17 \\ \hline
 $x-\overline x$     &  &  &  &  &  \\ \hline
 $(x-\overline x)^2$ &  &  &  &  &   \\
\hline
\end{tabular}\end{center}\end{table} \\
i3jW΍$s$߂B

process
i1j$\overline x=\displaystyle\frac{40}{5}=8$\\
i2j\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|ccccc|}
\hline
 $x$                     & 1 & 4 & 5 & 13 & 17 \\ \hline
 $x-\overline x$     & $-7$ & $-4$ & $-3$ & 5 & 9 \\ \hline
 $(x-\overline x)^2$ & 49 & 16 & 9 & 25 & 81  \\
\hline
\end{tabular}\end{center}\end{table} \\
 U$s^2=\displaystyle\frac{180}{5}=36$\\
i3jW΍$s=6$

i1j8Ci2j36Ci3j6

10l̐kɐw̃eXg{ƂC_̕ϓ_60_C
W΍20_łBƂ瑼1l̐k̐w̃eXg󂯂ƂC
_60_B1l11l̐kɂĕϒlƕW΍C
ꂼOƔׂƂC̐g\fbox{\,E\,}łB\\
\hspace{8pt} \textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|c||c|c|c|c|} \hline
                 & \textcircled{\small 1} & \textcircled{\small 2} & \textcircled{\small 3} & \textcircled{\small 4} \\ \hline \hline
    \scriptsize{\bf ϒl}@& \scriptsize{ςȂ} & \scriptsize{ςȂ} & \scriptsize{ςȂ} & \scriptsize{} \\ \hline
    \scriptsize{\bf W΍} & \scriptsize{ςȂ} & \scriptsize{} & \scriptsize{} & \scriptsize{ςȂ} \\ \hline
  \end{tabular}\end{center}
\end{table} \\
Cϗ$x$̃f[^̒l$x_1,x_2,\cdots,x_n$ŁC̕ϒl$\overline{x}$
̂ƂCW΍$s$\\
$s=\sqrt{\displaystyle\frac{\left( x_1-\overline{x} \right)^2+\left( x_2-\overline{x} \right)^2+\cdots+\left( x_n-\overline{x} \right)^2}{n}}$

process
ϒl͕ςȂB\\
^̕̕q̒l͕ωȂC11ɑ邽߁C
W΍$s$͏ȂB

\textcircled{\small 2}

O[vȀeXg̓_͎̒ʂłB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 _ & $4$ & $8$ & $10$ & $12$ & $16$\\ \hline
 ΍ &  &  &  &  & \\ \hline
 $΍^2$ &  &  &  &  & \\ \hline
\end{tabular}\end{center}\end{table}
}\\
i1jϒl$\overline x$߂B\\
i2j̕\̋󗓂𖄂߁CU$s^2$߂B\\
i3jW΍$s$߂B

process
i1j$\overline x=\displaystyle\frac{50}{5}=10$\\
i2j\\
U$s^2=\displaystyle\frac{36+4+0+4+36}{5}\\
=\displaystyle\frac{80}{5}=16$\\
i3jW΍$s=\sqrt{16}=4$

{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 _ & $4$ & $8$ & $10$ & $12$ & $16$\\ \hline
 ΍ & $-6$ & $-2$ & $0$ & $2$  & $6$ \\ \hline
 $΍^2$ & 36 & 4 & 0 & 4 & 36 \\ \hline
\end{tabular}\end{center}\end{table}}
i1j10Ci2j16Ci3j$4$

O[vB̏eXg̓_͎̒ʂłB\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 _ & $4$ & $7$ & $10$ & $13$ & $16$\\ \hline
 ΍ &  &  &  &  & \\ \hline
 $΍^2$ &  &  &  &  & \\ \hline
\end{tabular}\end{center}\end{table}}
 i1jϒl$\overline x$߂B\\
i2j̕\̋󗓂𖄂߁CU$s^2$߂B\\
i3jW΍$s$߂BC$\sqrt{2}=1.4$ƂB

process
i1j$\overline x=\displaystyle\frac{50}{5}=10$\\
i2j\\
U$s^2=\displaystyle\frac{36+9+0+9+36}{5}\\
=\displaystyle\frac{90}{5}=18$\\
i3jW΍$s=\sqrt{18}=3\sqrt{2}=3\times 1.4=4.2$

{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
 _ & $4$ & $7$ & $10$ & $13$ & $16$\\ \hline
 ΍ & $-6$ & $-3$ & $0$ & $3$  & $6$ \\ \hline
 $΍^2$ & 36 & 9 & 0 & 9 & 36 \\ \hline
\end{tabular}\end{center}\end{table}}
i1j10Ci2j18Ci3j$4.2$

̃f[^́C̈Ղ1N5NX񂾒꒵т̉񐔂l̏ɕׂ̂łB\\
i1jϒl$\overline x$߂B\\
i2j̕\̋󗓂𖄂߁CU$s^2$߂B\\
{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
  & $5$ & $8$ & $9$ & $11$ & $12$\\ \hline
 ΍ &  &  &  &  & \\ \hline
 $΍^2$ &  &  &  &  & \\ \hline
\end{tabular}\end{center}\end{table}}

process
i1j$\overline x=\displaystyle\frac{45}{5}=9$\\
i2jU$s^2=\displaystyle\frac{30}{5}\\
=6$

{\small
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 f[^ &  &  &  &  &  \\
 ԍ & 1 & 2 & 3 & 4 & 5  \\ \hline
  & $5$ & $8$ & $9$ & $11$ & $12$\\ \hline
 ΍ & $-4$ & $-1$ & 0 & 2 & 3 \\ \hline
 $΍^2$ & 16 & 1 & 0 & 4 & 9 \\ \hline
\end{tabular}\end{center}\end{table}}
i1j9Ci2j6

̃f[^́C鐶kƐw̏eXgꂼ
48s_̃f[^łB\\
\hspace{20pt} F3,\,4,\,4,\,5\\
\hspace{20pt} wF4,\,4,\,5,\,5,\,5,\,5,\,6,\,6i_j\\
\hspace{8pt} ̃f[^ɂĂ̋LqƂĐ̂
\fbox{\,E\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂IׁB\\
\textcircled{\small 1}\,ϒl͓CUB\\
\textcircled{\small 2}\,ϒl͓CU͐w̕傫B\\
\textcircled{\small 3}\,ϒl͐w̕傫CU͓B\\
\textcircled{\small 4}\,ϒl͐w̕傫CUw̕傫B\\
\hspace{8pt} Cϗ$x$̃f[^̒lC$x_1$C$x_2$C$\cdots$C$x_n$ŁC
̕ϒl$\overline{x}$̂ƂC
U$\displaystyle\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+\cdots +(x_n-\overline{x})^2}{n}$
ŋ߂B

process
Ǔ\\
$3|-[+4]-|5$C\\$4|-[+5]-|6$ɂ蕪U͂قړB\\
̕ϒl$\overline{x}=4$CU$=\displaystyle\frac{1}{2}$\\
w̕ϒl$\overline{x}=5$CU$=\displaystyle\frac{1}{2}$

\textcircled{\small 3}

\hspace{8pt} ̃f[^́CA1ɃerԂ7Ԓׂ̂łB\\
\hspace{12pt} $2,\,3,\,3,\,1,\,3,\,6,\,3$iԁj\\
\hspace{8pt} ̃f[^̕ϒl\fbox{\bf\,G\,}iԁjłCU
\fbox{\bf\,I\,}łB\\
\hspace{8pt} Cϗ$x$̃f[^̒lC$x_1$C$x_2$C$\cdots$C$x_n$ŁC
̕ϒl$\overline{x}$̂ƂC
U$\displaystyle\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+\cdots +(x_n-\overline{x})^2}{n}$
ŋ߂B

process
$\overline{x}=\displaystyle\frac{21}{7}=3$\\
$s^2=\displaystyle\frac{1+4+9}{7}=2$

ϒl$=3$CU$=2$

\hspace{8pt} 
̃f[^ I  I\hspace{-.1em}I ́C\ruby{告o}{||}̖11l̗͎mƏ\10l̗͎m̑̏dɕׂ̂łB\\
I: $135$,$155$,$155$,$158$,$168$,$168$,$172$,$175$,$181$,$186$,$197$ikgj\\
I\hspace{-.1em}I : $111$,$115$,$130$,$138$,$138$,$156$,$156$,$160$,$164$,$199$ikgj\\
II\hspace{-.1em}Ĩf[^̕ÚC1ʂľܓƁCꂼ$266$$609$łB\\
\hspace{8pt} 
̃f[^ɂĂ̋LqƂĐ̂\fbox{\,\bf E\,}łB
\textcircled{\small 1} $\sim$ \textcircled{\small 4}̂IׁB\\
\textcircled{\small 1}\,f[^͈̔͂I̕傫CW΍I
̕傫B\\
\textcircled{\small 2}\,f[^͈̔͂I\hspace{-.1em}I̕傫CW΍I\hspace{-.1em}I̕傫B\\
\textcircled{\small 3}\,f[^͈̔͂I̕傫CW΍I\hspace{-.1em}I̕傫B\\
\textcircled{\small 4}\,f[^͈̔͂I\hspace{-.1em}I̕傫CW΍ I ̕傫B

process
͈͂I:$197-135=62$CI\hspace{-.1em}I:$199-111=88$B\\
UI\hspace{-.1em}I̕傫̂ŕW΍I\hspace{-.1em}I̕傫B

\textcircled{\small 2}

̃f[^́C2̃TbJ[`[ACBŒ5őłV[g̖{łB\\
A:$4,5,5,5,6$i{j~~~B:$2,2,3,3,10$i{j\\
2̃f[^ɂĂ̋LqƂĐ̂\fbox{\,\bf G\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB
Cϗ$x$̃f[^̒l$x_1$C$x_2$C$\dots$C$x_n$ŁC
̕ϒl$\overline{x}$̂ƂCU\\
$\displaystyle\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2 \cdots +(x_n-\overline{x})^2}{n}$ŋ߂B\\
\textcircled{\small 1}\,ϒlUA̕傫B\\
\textcircled{\small 2}\,ϒlA̕傫CUB̕傫B\\
\textcircled{\small 3}\,ϒlB̕傫CUA̕傫B\\
\textcircled{\small 4}\,ϒlUB̕傫B

process
$\overline{x_A}=5$C$\overline{x_B}=4$C\\
Ǔڂ́C\\
$4|-[+5]-|6$\\
$2|-[+4]-|10$ɂC΂̍őĺC
A̕$1$CB͖̕$4$B̕傫CiUj$=$i΂j$^2$ 
B̕傫B\\
iQlj
$(s_A)^2=0.4$C$(s_B)^2=9.2$

\textcircled{\small 2}

̃f[^́C2l̐kACB󂯂w̏eXg5񕪂
_łB\\
${\rm A:\,3,\, 4,\, 5,\, 6,\, 7}$i_j~~~
${\rm B:\,2,\, 4,\, 5,\, 6,\, 8}$i_j\\
\hspace{8pt} ̃f[^ɂĂ̋LqƂĐ̂
\fbox{\bf\, E \,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂IׁB\\
\textcircled{\small 1}\,
ϒl͈قȂCUA̕傫B\\
\textcircled{\small 2}\,
ϒl͈قȂCUB̕傫B\\
\textcircled{\small 3}\,
ϒl͓CUA̕傫B\\
\textcircled{\small 4}\,
ϒl͓CUB̕傫B\\
\hspace{8pt} Cϗ$x$̃f[^̒l$x_1,\, x_2,\, \cdots ,\, x_n$ŁC̕ϒl$\overline{x}$̂ƂC
U
$\displaystyle\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2 +\cdots +(x_n-\overline{x})^2}{n}$
ŋ߂B

process
ϒl͓B\\
΂̌ڂ\\
$3|-[+5]-|7$\\
$2|-[+5]-|8$
B̕ϒl̃o傫B

\textcircled{\small 4}

̃f[^́Cv싅`[̍ŋ10
ł_${\rm X}$̒lłB
U$s^2$߂
\fbox{\hspace{8pt} 18 \hspace{8pt}}łB\\
\begin{table}[!hbt]
\begin{center}\begin{tabular}{|c|}
\hline
 f[^${\rm X}:\, 3,\,1,\,5,\,3,\,2,\,7,\,0,\,1,\,5,\,3$i_j \\
\hline
\end{tabular}\end{center}\end{table}
\textcircled{\small 1}\,$3$~~~
\textcircled{\small 2}\,$3.3$~~~
\textcircled{\small 3}\,$3.8$~~~
\textcircled{\small 4}\,$4.2$

process
$\overline{x}=3$C
$s^2=\displaystyle\frac{33}{10}=3.3$

\textcircled{\small 2}

̃f[^́CdC5ɂāC1̏[d
s\ȋ𒲂ׂ̂łB\\
\hspace{20pt}$280,\,295,\,300,\,320,\,305~~~({\rm km})$\\
\hspace{8pt} ̃f[^̕ϒl$300 ({\rm km})$łC
U\fbox{\bf\,JLN\,}łB
Cϗ$x$̃f[^̗ʂ
$x_1$C
$x_2$C$\cdots$C$x_n$ŁC
̕ϒl$\overline{x}$̂ƂCU\\
$\displaystyle\frac{(x_1 -\overline{x})^2+(x_2 -\overline{x})^2\cdots +(x_n -\overline{x})^2}{n}$ŋ߂B

process
$s^2=\displaystyle\frac{400+25+400+25}{5}=170$
\begin{table}[!hbt]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|}
\hline
 $x$ & 280 & 295 & 300 & 320 & 305 \\ \hline
 $x-\overline{x}$ & 20 & 5 & 0 & 20 & 5 \\ \hline
 $(x-\overline{x})^2$ & 400 & 25 & 0 & 400 & 25 \\ \hline
\end{tabular}\end{center}\end{table}

$170$

̃f[^́C
8l̐kɏĂ邩𒲍ʂłB\\
\hspace{20pt}$7,11,6,2,10,9,12,7$ij\\
̃f[^̕ϒl
\fbox{\bf\, E \,}ijŁCU
\fbox{\bf\, G \,}ijłB\\
\hspace{8pt}
Cϗ$x$̃f[^̒l$x_1,x_2,\cdots,x_n$ŁC
̕ϒl$\overline{x}$̂ƂC
U
$\displaystyle\frac{(x_1-\overline{x})^2+ (x_2-\overline{x})^2+\cdots +(x_n-\overline{x})^2}{n}$ŋ߂B
Kvł΁Cȉ̕\𗘗pȂB
\begin{table}[!hbt]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
  $x$                     & 7 & 11 & 6      & 2 & 10 & 9 & 12 & 7 \\ \hline
  $x-\overline{x}$ &  &  &  &  &  &  &  &  \\ \hline 
  $(x-\overline{x})^2$ &  &  &  &         &  &  &  &  \\ \hline
\end{tabular}\end{center}\end{table}

process
$\overline{x}=\displaystyle\frac{64}{8}=8$\\
$s^2=\displaystyle\frac{72}{8}=9$
\begin{table}[!hbt]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
  $x$                     & 7 & 11 & 6      & 2 & 10 & 9 & 12 & 7 \\ \hline
  $x-\overline{x}$ & $-1$ & 3 & $-2$ & $-6$ & 2 & 1 & 4 & $-1$ \\ \hline 
  $(x-\overline{x})^2$ & 1 & 9 & 4 & 36        & 4 & 1 & 16 & 1 \\ \hline
\end{tabular}\end{center}\end{table}

$\overline{x}=8$C$s^2=9$




[Level7]
֊֌Wibj
\hspace{8pt} ̎Uz}ɂāCΉ鑊֌WIтȂB\\
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=70mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/pic1361.eps}
 \end{center}\end{figure} 
 \begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline
  (1) & \hspace{16pt} & (2) & \hspace{16pt} & (3) & \hspace{16pt} & (4) & \hspace{16pt} \\ \hline
\end{tabular}\end{center} \end{table}\\
֌W\\
\textcircled{\small 1}\,0.9~~~
\textcircled{\small 2}\,0.5~~~
\textcircled{\small 3}\,$-0.8$~~~
\textcircled{\small 4}\,0

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline
  (1) & \textcircled{\small 4} & (2) & \textcircled{\small 2} & (3) & \textcircled{\small 3} &  (4) & \textcircled{\small 1} \\ \hline
\end{tabular}\end{center}\end{table}

̐}́CAgBg̒jqꂼ20l̃nh{[ƈ͂̋L^Uz}Ɏ̂łB\\
\hspace{8pt} 2̎Uz}ǂݎ邱Ƃ\fbox{\,G\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂łK؂Ȃ̂IׁB\\
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=70mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2702m0602.eps}
 \end{center}\end{figure} \\
\textcircled{\small 1}\,nh{[ƈ͂̋L^ɂ́C̑ւB\\
\textcircled{\small 2}\,nh{[ƈ͂̋L^ɂ́C̑ւB\\
\textcircled{\small 3}\,nh{[ƈ͂̋L^ɂ́CւȂB\\
\textcircled{\small 4}\,Ag̋L^Bg̋L^ł̓f[^̌XႤ̂ŁCnh{[ƈ͂̋L^ɂĔfł鎖͂ȂB

\textcircled{\small 1}

̕\́C10l̐kɊƉpP̃eXgsʂłB\\
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|c||c|c|c|c|c|c|c|c|c|c|} \hline
    {\footnotesize k}        & A & B & C & D & E & F & G & H & I & J \\ \hline
    {\footnotesize } &  &  &  &  &  &  &  &  &  &  \\ 
    {\footnotesize i_j} & 4 & 6 & 8 & 5 & 6 & 8 & 9 & 4 & 3 & 4 \\ \hline
    {\footnotesize pP} &  &  &  &  &  &  &  &  &  &  \\ 
 {\footnotesize i_j} & 5 & 5 & 10 & 6 & 2 & 2 & 9 & 2 & 3 & 7 \\ \hline
  \end{tabular}\end{center}
\end{table}
\hspace{8pt} ̌ʂ̎Uz}ƂčłK؂Ȃ̂\fbox{\,G\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
  \begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2701m0605.eps}
 \end{center}\end{figure} 

\textcircled{\small 4}

̎Uz}ÁC鐶k10l̍Ɖp̏eXǧʂ\̂łC
Uz}B́C10l̐kɂčƐw̏eXǧʂ\̂łB
ƉpCƐw̏eXg̑֊֌WɂčłK؂Ȃ̂\fbox{\,G\,}łB\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2602m0602.eps}
 \end{center}\end{figure} \\
\textcircled{\small 1}\,ƉpCƐẃCƂɑւB\\
\textcircled{\small 2}\,ƉpCƐẃCƂɑւアB\\
\textcircled{\small 3}\,Ɖp͐̑ւCƐw͕̑ւB\\
\textcircled{\small 4}\,Ɖp͐̑ւCƐw͑ւアB

\textcircled{\small 4}

X4ނ̏i1̔̔ꂼ20ԒׂB
́iAj$\sim$iDj̎Uz}1̍ōC$x(^\circ C)$Ɣ̔$y$ij̊֌W\̂łB4ނ̃f[^ɂ$x$$y$̑֊֌Wɂ
{\bf Ă}\fbox{\,G\,}łB\\
\hspace{8pt}
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2601m0602.eps}
 \end{center}\end{figure} \\
\textcircled{\small 1}\,iAj͐̑ւC֌W͐̒lƂB\\
\textcircled{\small 2}\,iBjiAj̕֌W͑傫B\\
\textcircled{\small 3}\,iCj̑֌ẂiDj̑֌Wɔׂ$0$ɋ߂lƂB\\
\textcircled{\small 4}\,iAjƁiDj͂ւC֌W͑̃f[^ɔׂ$1$ɋ߂ȂB

\textcircled{\small 4}

̎Uz}ɂāCϗ$x$$y$̑֌WƂčłK؂Ȃ̂\fbox{\,G\,}
łB\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\textcircled{\small 1}\,$0.9$~~~
\textcircled{\small 2}\,$0.3$~~~
\textcircled{\small 3}\,$-0.1$~~~
\textcircled{\small 4}\,$-0.6$
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=40mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2802m0603.eps}
 \end{center}\end{figure} 

\textcircled{\small 4}

\hspace{8pt}
2̕ϗ$x$$y$Ȃf[^ɂđ֌W$-0.72$łB
̃f[^̎Uz}ƂčłK؂Ȃ̂\fbox{\bf\,J\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=60mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2801m0603.eps}
 \end{center}\end{figure} 

\textcircled{\small 4}

̎Uz}ɊւLq̋󗓂ɓׂK؂Ȏ𓚌Q
IׁB\\
\hspace{8pt} 
cƉɊ֘ÂQ̓ƂCl_ŏނ̂ŁC_̎U
΂ɂāCQ̓̑֊֌W邱ƂłB}Q̂悤ȂR
̃Ot̂ƂC֊֌W\fbox{\,\textcircled{\small 3}\,}ƂB\\
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/H2501j102.eps}
 \end{center}\end{figure} 
{\bf \textcircled{\small 3}̉𓚌Q}\\
{\bf A}D͐̑ւC͑ւȂC͕̑ւ\\
{\bf C}D͕̑ւC͑ւȂC͐̑ւ\\
{\bf E}DPԑւ\\
{\bf G}DׂĂɑւ

C

̎Uz}(A)C(B)C(C)C(D)ɑΉ鑊֌Wꂼ
$a$C$b$C$c$C$d$łƂC֌W̑召֌WƂĐ̂\fbox{\,\bf G\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\textcircled{\small 1}\,$a<b<c<d$~~~
\textcircled{\small 2}\,$b<d<c<a$\\
\textcircled{\small 3}\,$d<b<a<c$~~~
\textcircled{\small 4}\,$b<d<a<c$
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2901m602.eps}
 \end{center}\end{figure} 

\textcircled{\small 4}

}́CNX̐k20lɑ΂čswƉp̃eXg̓_Uz}Ƃĕ\̂łB̎Uz}ɂĂ̋LqƂ{\bf K؂łȂ}\fbox{\,\bf I\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}̂IׁB\\
\textcircled{\small 1}\,wƉp̂ǂ60_ȏł鐶k8lłB\\
\textcircled{\small 2}\,w̓_͈̔͂̕Cp̓_͈̔͂傫B\\
\textcircled{\small 3}\,w̓_20_
k͉p̓_40_ȏłB\\
\textcircled{\small 4}\,
wƉp̓_̊Ԃɂ͐̑ւB
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h2902m602.eps}
 \end{center}\end{figure} 

process
\textcircled{\small 1}\,ǂ60_ȏ7lB\\
\textcircled{\small 2}\,w͈̔$\fallingdotseq 100-15=85$Cp͈̔$\fallingdotseq 92-27=65$

\textcircled{\small 1}

E̐}́CoXPbg{[̂15`[ɂāC
1̃V[g̖{̕ϒl$x$i{jƓ_̕ϒl$y$i_j
Uz}ɕ\̂łB
}̎Uz}ɂāC$x$$y$̑֌WƂčłK؂Ȃ̂
\fbox{\bf\hspace{4pt} G \hspace{4pt}}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂IׁB\\
\textcircled{\small 1}\,$0.9$~~~
\textcircled{\small 2}\,$0.4$~~~
\textcircled{\small 3}\,$-0.5$~~~
\textcircled{\small 4}\,$-0.9$
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=40mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h3001603.eps}
 \end{center}\end{figure} 

\textcircled{\small 2}

̎Uz}ÁCss10ɂ
ōCƍŒC\̂łC
Uz}B́Cssœɂ̍ōC
ώx\̂łB
̎Uz}ɊւLqƂčłK؂Ȃ̂\fbox{\bf\, P \,}
łB\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂IׁB\\
\textcircled{\small 1}\,
ōCƍŒCCōCƕώx́CƂɐ̑֊֌WB\\
\textcircled{\small 2}\,
ōCƍŒCCōCƕώx́CƂɕ̑֊֌WB\\
\textcircled{\small 3}\,
ōCƍŒC͑֊֌WC
ōCƕώx́CƂɑ֊֌WアB\\
\textcircled{\small 4}\,
ōCƍŒC͑֊֌WキC
ōCƕώx́CƂɑ֊֌WB
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=76mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h3002m602.eps}
 \end{center}\end{figure} 

\textcircled{\small 3}

̐}́C{̂12ss̖k$x$ixjƔNԕϋC$y$i${}^\circ$Cj
̃f[^̎Uz}łB
$x$$y$̑֌W̋ߎlƂāCłK؂Ȃ̂\fbox{\bf\, I\,}łB
\textcircled{\small 1}$\sim$\textcircled{\small 4}
̂IׁB\\
\textcircled{\small 1}\,$0.95$~~~
\textcircled{\small 2}\,$0.29$~~~
\textcircled{\small 3}\,$-0.33$~~~
\textcircled{\small 4}\,$-0.99$
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=60mm,clip]{D:/texlive/2018/bin/win32/mathtex/303_data/h31m604.eps}
 \end{center}\end{figure} 

\textcircled{\small 4}







[Level8]
֊֌WvZi1iŎgp邱Ɓj
ϗ$x,\,y$̕\ŗ^ƂC̕\C$x$$y$̑֌W$r$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  $x$ & 2 & 3 & 4 \\ \hline
  $y$ & 1 & 3 & 5 \\ \hline
\end{tabular}\end{center}\end{table}\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic111.tex}
\end{center}
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 4     &                 &                 &                     &                     &             \\ \hline
   & 3 & 3     &                 &                 &                     &                      &            \\ \hline
   & 4 & 2     &                 &                 &                     &                       &           \\ \hline \hline
  a &  &      & ^                & ^                &                     &                        &          \\ \hline
   &  &      & ^                & ^                &                     &                       &           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}

process
֌W\\$r=\displaystyle\frac{s_{xy}}{s_{x}s_{y}}
=-\displaystyle\frac{2}{3}\div \left( \sqrt{\displaystyle\frac{2}{3}} \times \sqrt{\displaystyle\frac{2}{3}} \right)=-1$

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 4     & $-1$           & $1$              & $1$                 & $1$                 & $-1$           \\ \hline
   & 3 & 3     & $0$            & $0$              & $0$                 & $0$                 & $0$            \\ \hline
   & 4 & 2     & $1$            & $-1$             & $1$                 & $1$                 & $-1$           \\ \hline \hline
  a & $9$ & $9$ & ^          & ^              & $2$                 & $2$                 & $-2$          \\ \hline
   & $3$ & $3$  & ^       & ^              & $\displaystyle\frac{2}{3}$  & $\displaystyle\frac{2}{3}$ & $-\displaystyle\frac{2}{3}$           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}\\
$r=-1$

ϗ$x,\,y$̕\ŗ^ƂC̕\C$x$$y$̑֌W$r$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  $x$ & 2 & 3 & 4 \\ \hline
  $y$ & 1 & 3 & 5 \\ \hline
\end{tabular}\end{center}\end{table}\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic112.tex}
\end{center}
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 1     &                 &                 &                     &                     &             \\ \hline
   & 3 & 3     &                 &                 &                     &                      &            \\ \hline
   & 4 & 5     &                 &                 &                     &                       &           \\ \hline \hline
  a &  &      & ^                & ^                &                     &                        &          \\ \hline
   &  &      & ^                & ^                &                     &                       &           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}

process
֌W\\$r=\displaystyle\frac{s_{xy}}{s_{x}s_{y}}
=\displaystyle\frac{4}{3}\div \left( \sqrt{\displaystyle\frac{2}{3}} \times \sqrt{\displaystyle\frac{8}{3}} \right)
=\displaystyle\frac{4}{3}\div\displaystyle\frac{4}{3}=1$

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 1     & $-1$           & $-2$              & $1$                 & $4$                 & $2$           \\ \hline
   & 3 & 3     & $0$            & $0$              & $0$                 & $0$                 & $0$            \\ \hline
   & 4 & 5     & $1$            & $2$             & $1$                 & $4$                 & $2$           \\ \hline \hline
  a & $9$ & $9$    & ^       & ^              & $2$                 & $8$                 & $4$          \\ \hline
   & $3$ & $3$  & ^       & ^      & $\displaystyle\frac{2}{3}$  & $\displaystyle\frac{8}{3}$ & $\displaystyle\frac{4}{3}$           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}\\
$r=1$

ϗ$x,\,y$̕\ŗ^ƂC̕\C$x$$y$̑֌W$r$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  $x$ & 2 & 3 & 4 \\ \hline
  $y$ & 3 & 2 & 4 \\ \hline
\end{tabular}\end{center}\end{table}\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic113.tex}
\end{center}
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 3     &                 &                 &                     &                     &             \\ \hline
   & 3 & 2     &                 &                 &                     &                      &            \\ \hline
   & 4 & 4     &                 &                 &                     &                       &           \\ \hline \hline
  a &  &      & ^                & ^                &                     &                        &          \\ \hline
   &  &      & ^                & ^                &                     &                       &           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}

process
֌W\\$r=\displaystyle\frac{s_{xy}}{s_{x}s_{y}}
=\displaystyle\frac{1}{3}\div \left( \sqrt{\displaystyle\frac{2}{3}} \times \sqrt{\displaystyle\frac{2}{3}} \right)
=\displaystyle\frac{1}{3}\div\displaystyle\frac{2}{3}=\displaystyle\frac{1}{2}=0.5$

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 3     & $-1$           & $0$              & $1$                 & $0$                 & $0$           \\ \hline
   & 3 & 2     & $0$            & $-1$              & $0$                 & $1$                 & $0$            \\ \hline
   & 4 & 4     & $1$            & $1$             & $1$                 & $1$                 & $1$           \\ \hline \hline
  a & $9$ & $9$    & ^       & ^              & $2$                 & $2$                 & $1$          \\ \hline
   & $3$ & $3$  & ^       & ^ & $\displaystyle\frac{2}{3}$  & $\displaystyle\frac{2}{3}$ & $\displaystyle\frac{1}{3}$           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}\\
$r=\displaystyle\frac{1}{2}=0.5$

ϗ$x,\,y$̕\ŗ^ƂC̕\C$x$$y$̑֌W$r$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|}
 \hline
  $x$ & 2 & 3 & 4 \\ \hline
  $y$ & 4 & 2 & 3 \\ \hline
\end{tabular}\end{center}\end{table}\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic114.tex}
\end{center}
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 4     &                 &                 &                     &                     &             \\ \hline
   & 3 & 2     &                 &                 &                     &                      &            \\ \hline
   & 4 & 3     &                 &                 &                     &                       &           \\ \hline \hline
  a &  &      & ^                & ^                &                     &                        &          \\ \hline
   &  &      & ^                & ^                &                     &                       &           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}

process
֌W\\$r=\displaystyle\frac{s_{xy}}{s_{x}s_{y}}
=-\displaystyle\frac{1}{3}\div \left( \sqrt{\displaystyle\frac{2}{3}} \times \sqrt{\displaystyle\frac{2}{3}} \right)
=-\displaystyle\frac{1}{3}\div\displaystyle\frac{2}{3}=-\displaystyle\frac{1}{2}=-0.5$

\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 4     & $-1$           & $1$              & $1$                 & $1$                 & $-1$           \\ \hline
   & 3 & 2     & $0$            & $-1$              & $0$                 & $1$                 & $0$            \\ \hline
   & 4 & 3     & $1$            & $0$             & $1$                 & $0$                 & $0$           \\ \hline \hline
  a & $9$ & $9$    & ^       & ^              & $2$                 & $2$                 & $-1$          \\ \hline
   & $3$ & $3$  & ^       & ^ & $\displaystyle\frac{2}{3}$  & $\displaystyle\frac{2}{3}$ & $-\displaystyle\frac{1}{3}$           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}\\
$r=-\displaystyle\frac{1}{2}=-0.5$

ϗ$x,\,y$̕\ŗ^ƂC̕\C$x$$y$̑֌W$r$߂B\\
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|}
 \hline
  $x$ & 2 & 3 & 4 & 3\\ \hline
  $y$ & 4 & 5 & 2 & 1\\ \hline
\end{tabular}\end{center}\end{table}\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/303_data/pic117.tex}
\end{center}
\begin{table}[!htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 4     &                 &                 &                     &                     &             \\ \hline
   & 3 & 5     &                 &                 &                     &                      &            \\ \hline
   & 4 & 2     &                 &                 &                     &                      &            \\ \hline 
   & 3 & 1     &                 &                 &                     &                       &           \\ \hline \hline
  a &  &      & ^                & ^                &                     &                        &          \\ \hline
   &  &      & ^                & ^                &                     &                       &           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}

process
֌W\\$r=\displaystyle\frac{s_{xy}}{s_{x}s_{y}}
=-\displaystyle\frac{1}{2}\div \left( \sqrt{\displaystyle\frac{1}{2}} \times \sqrt{\displaystyle\frac{5}{2}} \right)
=-\displaystyle\frac{1}{2}\div\displaystyle\frac{\sqrt{5}}{2}=-\displaystyle\frac{\sqrt{5}}{5}$

\begin{table}[htb]
\begin{center}\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline
   & $x$ & $y$ & $x-\overline x$ & $y-\overline y$ & $(x-\overline x)^2$ & $(y-\overline y)^2$ & $(x-\overline x)(y-\overline y)$ \\ \hline
   & 2 & 4     & $-1$           & $1$              & $1$                 & $1$                 & $-1$           \\ \hline
   & 3 & 5     & $0$            & $2$              & $0$                 & $4$                 & $0$            \\ \hline
   & 4 & 2     &  $1$           & $-1$             & $1$                 & $1$                 & $-1$          \\ \hline
   & 3 & 1     & $0$            & $-2$             & $0$                 & $4$                 & $0$           \\ \hline \hline
  a & $12$ & $12$    & ^       & ^              & $2$                 & $10$                 & $-2$          \\ \hline
   & $3$ & $3$  & ^       & ^ & $\displaystyle\frac{1}{2}$  & $\displaystyle\frac{5}{2}$ & $-\displaystyle\frac{1}{2}$           \\ \hline
  ^ & $\overline x$ & $\overline y$ & ^         & ^                  & $s_x^2$ & $s_y^2$ & $s_{xy}$ \\ \hline
\end{tabular}\end{center}\end{table}\\
$r=-\displaystyle\frac{\sqrt{5}}{5}$






[EOF]
% t@C̍Ōɂ

