$\begin{array}{ll} 51.&\textrm{Simpangan kuartil dari data}\\ &5\: \: 6\: \: a\: \: 3\: \: 7\: \: 8\: \: \textrm{adalah}\: \: 1\displaystyle \frac{1}{2}.\: \textrm{Jika median datanya}\\ & \textrm{adalah}\: \: 5\displaystyle \frac{1}{2},\: \textrm{maka rata-rata data}\: \: \textrm{tersebut adalah}\: ....\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{4}&&&\textrm{d}.&\textrm{5}\displaystyle \frac{1}{2}\\ \textrm{b}.&\textrm{4}\displaystyle \frac{1}{2}\quad &\textrm{c}.&\textrm{5}\quad&\textrm{e}.&\textrm{6} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{d}\\ &\begin{aligned} &\color{blue}\textrm{Diketahui data sebagai berikut}\\ &5\: \: 6\: \: a\: \: 3\: \: 7\: \: 8\: \Rightarrow \: n=6\\&\color{red}\textrm{karena mediannya}=M_{e}=Q_{2}=5\frac{1}{2}=\frac{11}{2}\\&\color{blue}\textrm{ data menjadi}\: :\: \color{black}a\: \: 3\: \: 5\: \: 6\: \: 7\: \: 8\: \: \color{blue}\textrm{atau}\color{black}\: \: 3\: \: a\: \: 5\: \: 6\: \: 7\: \: 8\\ &\textrm{Simpangan kuartilnya adalah}\: 1\displaystyle \frac{1}{2}=\displaystyle \frac{3}{2}\\ &Q_{d}=\displaystyle \frac{1}{2}\left (Q_{3}-Q_{1} \right ) =\displaystyle \frac{3}{2}\: \Rightarrow\: Q_{3}-Q_{1}=3\\&\textrm{maka}\\ &3=Q_{3}-Q_{1}=x_{._{\frac{3}{4}n+\frac{1}{2}}}-x_{._{\frac{1}{4}n+\frac{1}{2}}}=x_{._{\frac{3}{4}6+\frac{1}{2}}}-x_{._{\frac{1}{4}6+\frac{1}{2}}} \\ &\quad\: =\left (x_{._{5}}-x_{._{2}} \right )=7-x_{._{2}}=\color{red}3\: \color{black}\Rightarrow\: x_{._{2}}=4\\ &\textrm{Jadi, rata-ratanya adalah}:\\ &\overline{x}=\frac{3+4+5+6+7+8}{6}=\color{red}5,5 \end{aligned} \end{array}$.
$\begin{array}{ll} 52.&\textrm{Simpangan kuartil dari data}\\ &\textrm{berikut}\\ &61,61,50,50,53,53,70,61\\ &53,70,53,61,50,61,70\\ &\textrm{adalah}\: ....\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{10}&&&\textrm{d}.&\textrm{6}\\ \textrm{b}.&\textrm{9}\quad &\textrm{c}.&\textrm{8}\quad&\textrm{e}.&\textrm{5} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{-}\\ &\begin{aligned} &\color{red}\textrm{Data mula-mula}\: \: \color{black}n=15\\ &61,61,50,50,53,53,70,61\\ &53,70,53,61,50,61,70\\ &\color{blue}\textrm{data durutkan}\\ &50,50,50,53,53,53,53\\ &61,61,61,61,61,70,70,70\\ &\textrm{Simpangan kuartil adalah}\: Q_{d},\\ &Q_{d}=\displaystyle \frac{1}{2}\left ( Q_{3}-Q_{1} \right )\\ &\quad\: =\displaystyle \frac{1}{2}\left ( x_{._{\frac{3}{4}(n+1)}}-x_{._{\frac{1}{4}(n+1)}} \right )\\ &\quad\: =\displaystyle \frac{1}{2}\left ( x_{._{\frac{3}{4}(15+1)}}-x_{._{\frac{1}{4}(15+1)}} \right )\\ &\quad\: =\displaystyle \frac{1}{2}\left ( x_{._{12}}-x_{._{4}} \right )\\ &\quad\: =\displaystyle \frac{1}{2}\left ( 61-53 \right )=\displaystyle \frac{1}{2}\times 8=4\\ &\textrm{Jadi},\: Q_{d}=4 \end{aligned} \end{array}$.
$\begin{array}{ll} 53.&\textrm{Simpangan rata-rata dari data berikut}:\\ &6\quad 4\quad 2\quad 8\quad 10\quad\textrm{ adalah}\: ....\\\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{2}&&&\textrm{d}.&\textrm{3},0\\ \textrm{b}.&\textrm{2},4\quad &\textrm{c}.&\textrm{2},5\quad&\textrm{e}.&\textrm{3},5 \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{b}\\ &\begin{aligned} &\color{blue}\textrm{Diketahui data sebagai berikut}\\ &6\quad 4\quad 2\quad 8\quad 10\quad \\ &\textrm{Simpangan rata-ratanya adalah}: \\ &SR=\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n}\left | x_{i}-\overline{x} \right |\\&\textrm{dengan}\\ & \overline{x}=\displaystyle \frac{6+4+2+8+10}{5}=\displaystyle \frac{30}{5}=\color{red}6 \\ &\textrm{maka nilai}\\ &SR=\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n}\left | x_{i}-\overline{x} \right |\\ &\: \: \: \quad =\displaystyle \frac{1}{5}\left( \left| 6-6 \right|+\left| 4-6 \right|+\left| 2-6 \right|+\left| 8-6 \right|+\left| 10-6 \right| \right)\\ &\: \: \: \quad =\displaystyle \frac{1}{5}\left( \left| 0 \right|+\left| -2 \right|+\left| -4 \right|+\left| 2 \right|+\left| 4 \right| \right)\\ &\: \: \: \quad =\displaystyle \frac{1}{5}\left( 0+2+4+2+4 \right)\\ &\: \: \: \quad =\displaystyle \frac{1}{5}(12)=\displaystyle \frac{12}{5}=\color{red}2,4\\ \end{aligned} \end{array}$.
$\begin{array}{ll} 54.&\textrm{Simpangan rata-rata dari data berikut}:\\ &10,8,7,10,7,5,8,6,10,9\quad\textrm{ adalah}\: ....\\\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{1,0}&&&\textrm{d}.&\textrm{8,0}\\ \textrm{b}.&\textrm{1,4}\quad &\textrm{c}.&\textrm{6,0}\quad&\textrm{e}.&\textrm{14,0} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{b}\\ &\begin{aligned} &\color{blue}\textrm{Diketahui data sebagai berikut}\\ &10,8,7,10,7,5,8,6,10,9\quad \\ &\textrm{Simpangan rata-ratanya adalah}: \\ &SR=\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n}\left | x_{i}-\overline{x} \right |\\&\textrm{dengan}\\ & \overline{x}=\displaystyle \frac{10+8+7+10+7+5+8+6+10+9}{10}\\ &\: \: \: \, =\displaystyle \frac{80}{10}=\color{red}8 \\ &\textrm{maka nilai}\\ &SR=\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n}\left | x_{i}-\overline{x} \right |\\ &\: \: \: \quad =\displaystyle \frac{1}{10}\left( \left| 5-8 \right|+\left| 6-8 \right|+2\left| 7-8 \right|+2\left| 8-8 \right|+\left| 9-8 \right|+3\left| 10-8 \right| \right)\\ &\: \: \: \quad =\displaystyle \frac{1}{10}\left( \left| -3 \right|+\left| -2 \right|+2\left| -1 \right|+2\left| 0 \right|+\left| 1 \right|+3\left| 2 \right| \right)\\ &\: \: \: \quad =\displaystyle \frac{1}{10}\left( 3+2+2+0+1+6 \right)\\ &\: \: \: \quad =\displaystyle \frac{1}{10}(14)=\displaystyle \frac{14}{10}=\color{red}1,4\\ \end{aligned} \end{array}$.
$\begin{array}{ll} 55.&\textrm{Nilai variansi dari data}\\ &6,7,7,8,8,8,8,12\textrm{ adalah}\: ....\\\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{1}&&&\textrm{d}.&\textrm{8}\\ \textrm{b}.&\displaystyle \frac{26}{8}\quad &\textrm{c}.&\displaystyle \frac{11}{4}\quad&\textrm{e}.&\textrm{22} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{c}\\ &\begin{aligned} &\color{blue}\textrm{Diketahui data sebagai berikut}\\ &6,7,7,8,8,8,8,12\quad \\ &\textrm{Variannya adalah}: \\ &S^{2}=\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} \\&\textrm{dengan}\\ & \overline{x}=\displaystyle \frac{6+7+7+8+8+8+8+12}{8}=\displaystyle \frac{64}{8}=\color{red}8 \\ &\textrm{maka nilai}\\ &S^{2}=\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} \\ &\: \: \: \quad =\displaystyle \frac{1}{8}\left( (6-8)^{2}+2(7-6)^{2}+4(8-8)^{2}+(12-8)^{2} \right)\\ &\: \: \: \quad =\displaystyle \frac{1}{8}\left( 2^{2}+2.1+4.0+4^{2} \right)\\ &\: \: \: \quad =\displaystyle \frac{1}{8}\left( 4+2+0+16 \right)\\ &\: \: \: \quad =\displaystyle \frac{1}{8}(22)=\color{red}\displaystyle \frac{11}{4}=\color{black}2,75\\ \end{aligned} \end{array}$.
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