Contoh Soal 13 Statistika

$\begin{array}{ll} 56.&\textrm{Simpangan baku dari data berikut}:\\ &6,7,4,5,3\quad\textrm{ adalah}\: ....\\\\ &\begin{array}{lllllll} \textrm{a}.&\displaystyle \frac{1}{2}&&&\textrm{d}.&\sqrt{2}\\ \textrm{b}.&\displaystyle \frac{1}{2}\sqrt{2}\quad &\textrm{c}.&\displaystyle \frac{1}{2}\sqrt{3}\quad&\textrm{e}.&\sqrt{3} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{d}\\ &\begin{aligned} &\color{blue}\textrm{Diketahui data sebagai berikut}\\ &6,7,4,5,3\quad \\ &\textrm{Simpangan bakuya adalah}: \\ &S=\sqrt{S^{2}}=\sqrt{\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} }\\&\textrm{dengan}\\ & \overline{x}=\displaystyle \frac{6+7+4+5+3}{5}=\displaystyle \frac{25}{5}=\color{red}5 \\ &\textrm{maka nilai}\\ &S=\sqrt{\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} }\\ & \quad =\sqrt{\displaystyle \frac{1}{5}\left((6-5)^{2}+(7-5)^{2}+(4-5)^{2}+(5-5)^{2}+(3-5)^{2} \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{5}\left(1^{2}+2^{2}+1^{2}+0+2^{2} \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{5}\left( 1+4+1+4 \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{5}(10)}=\sqrt{\displaystyle \frac{10}{5}}=\color{red}\sqrt{2}\\ \end{aligned} \end{array}$.

$\begin{array}{ll} 57.&\textbf{UN 2010}\\ &\textrm{Simpangan baku dari data berikut}:\\ &2,3,4,5,6\quad\textrm{ adalah}\: ....\\\\ &\begin{array}{lllllll} \textrm{a}.&\sqrt{15}&&&\textrm{d}.&\sqrt{3}\\ \textrm{b}.&\displaystyle \sqrt{10}\quad &\textrm{c}.&\displaystyle \sqrt{5}\quad&\textrm{e}.&\sqrt{2} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{d}\\ &\begin{aligned} &\color{blue}\textrm{Diketahui data sebagai berikut}\\ &2,3,4,5,6\quad \\ &\textrm{Simpangan bakuya adalah}: \\ &S=\sqrt{S^{2}}=\sqrt{\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} }\\&\textrm{dengan}\\ & \overline{x}=\displaystyle \frac{2+3+4+5+6}{5}=\displaystyle \frac{20}{5}=\color{red}4 \\ &\textrm{maka nilai}\\ &S=\sqrt{\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} }\\ & \quad =\sqrt{\displaystyle \frac{1}{5}\left((2-5)^{2}+(3-5)^{2}+(4-5)^{2}+(5-5)^{2}+(6-5)^{2} \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{5}\left(3^{2}+2^{2}+1^{2}+0+1^{2} \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{5}\left( 9+4+1+1 \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{5}(15)}=\sqrt{\displaystyle \frac{15}{5}}=\color{red}\sqrt{3}\\ \end{aligned} \end{array}$.

$\begin{array}{ll} 58.&\textrm{Simpangan baku dari data berikut}:\\ &7,9,11,13,15\quad\textrm{ adalah}\: ....\\\\ &\begin{array}{lllllll} \textrm{a}.&2,4&&&\textrm{d}.&2,8\\ \textrm{b}.&\displaystyle 2,5\quad &\textrm{c}.&\displaystyle 2,7\quad&\textrm{e}.&2,9 \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{d}\\ &\begin{aligned} &\color{blue}\textrm{Diketahui data sebagai berikut}\\ &7,9,11,13,15\quad \\ &\textrm{Simpangan bakuya adalah}: \\ &S=\sqrt{S^{2}}=\sqrt{\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} }\\&\textrm{dengan}\\ & \overline{x}=\displaystyle \frac{7+9+11+13+15}{5}=\displaystyle \frac{55}{5}=\color{red}11 \\ &\textrm{maka nilai}\\ &S=\sqrt{\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} }\\ & \quad =\sqrt{\displaystyle \frac{1}{5}\left((7-11)^{2}+(9-11)^{2}+(11-11)^{2}+(13-11)^{2}+(15-11)^{2} \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{5}\left(4^{2}+2^{2}+0+2^{2}+4^{2} \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{5}\left( 16+4+4+16 \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{5}(40)}=\sqrt{\displaystyle \frac{40}{5}}=\color{red}\sqrt{8}=2,82..\\ \end{aligned} \end{array}$.

 $\begin{array}{ll} 59.&\textrm{Simpangan baku dari data berikut}:\\ &2,4,4,5,6,6,7,8,9,9\quad\textrm{ adalah}\: ....\\\\ &\begin{array}{lllllll} \textrm{a}.&4\sqrt{3}&&&\textrm{d}.&\displaystyle \frac{2}{5}\sqrt{30}\\ \textrm{b}.&2\displaystyle \frac{2}{5}\quad &\textrm{c}.&\displaystyle \sqrt{5}\quad&\textrm{e}.&2 \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{d}\\ &\begin{aligned} &\color{blue}\textrm{Diketahui data sebagai berikut}\\ &2,4,4,5,6,6,7,8,9,9\quad \\ &\textrm{Simpangan bakunya adalah}: \\ &S=\sqrt{S^{2}}=\sqrt{\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} }\\&\textrm{dengan}\\ & \overline{x}=\displaystyle \frac{2+4+4+5+6+6+7+8+9+9}{10}=\displaystyle \frac{60}{10}=\color{red}6 \\ &\textrm{maka nilai}\\ &S=\sqrt{\displaystyle \frac{1}{n}\displaystyle \sum_{i=1}^{n} \left( x_{i}-\overline{x} \right)^{2} }\\ & \quad =\sqrt{\displaystyle \frac{1}{10}\left((2-6)^{2}+2(4-6)^{2}+(5-6)^{2}+2(6-6)^{2}+(7-6)^{2}+(8-6)^{2}+2(9-6)^{2} \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{10}\left(4^{2}+2.2^{2}+1^{2}+0+1^{2}+2^{2}+2.3^{2} \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{10}\left( 16+8+1+1+4+18 \right)}\\ & \quad =\sqrt{\displaystyle \frac{1}{10}(48)}=\sqrt{\displaystyle \frac{48}{10}}=\sqrt{\displaystyle \frac{120}{25}}=\color{red}\displaystyle \frac{2}{5}\sqrt{30}\\ \end{aligned} \end{array}$.