Contoh Soal 11 Statistika

$\begin{array}{ll} 46.&\textrm{Rata-rata dari data yang disajikan }\\ &\textrm{dengan hitogram berikut adalah}\: ....\\   \end{array}$.

$.\qquad\begin{array}{ll} &\begin{array}{lllllll}\\ \textrm{a}.&41,372&&&\textrm{d}.&43,135\\ \textrm{b}.&42,150\quad&\textrm{c}.&43,125\quad&\textrm{e}.&44,250 \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textbf{c}\\ &\begin{aligned} &\begin{array}{|c|c|c|c|}\hline \begin{aligned}&\textrm{Berat}\\ &\textrm{Badan} \end{aligned}&\color{red}\textrm{f}_{1}&\begin{aligned}&\textrm{Nilai Tengah}\\ &\qquad(\textrm{x}_{1}) \end{aligned}&\color{red}\textrm{f}_{1}\textrm{x}_{1}\\\hline 30-34&5&32&160\\ 35-39&7&37&259\\ 40-44&12&42&504\\ 45-49&9&47&423\\ 50-54&4&52&208\\ 55-59&3&57&171\\\hline &\sum \textrm{f}_{1}=\color{red}40&&\sum \textrm{f}_{1}\textrm{x}_{1}=\color{red}1725\\\hline \end{array}\\ &\textrm{maka nilai dari}\: \: \overline{\textrm{x}}\: \: \textrm{adalah}:\\ &\overline{\textrm{x}}=\displaystyle \frac{\sum \textrm{f}_{1}\textrm{x}_{1}}{\sum \textrm{f}_{1}}=\displaystyle \frac{1725}{40}=\color{red}43,125 \end{aligned}  \end{array}$.

$\begin{array}{ll} 47.&(\textbf{UN Mat IPA 2006})\\ &\textrm{Perhatikan gambar berikut}\end{array}$.

$.\qquad\begin{array}{ll} &\textrm{Berat badan pada suatu kelas tersaji dengan}\\ &\textrm{bentuk histogram seperti pada gambar di atas}\\ &\textrm{Rata-rata berat badan tersebut adalah}\: ....\: \textrm{Kg}\\ &\begin{array}{lllllll}\\ \textrm{a}.&64,5&&&\textrm{d}.&66\\ \textrm{b}.&65\quad&\textrm{c}.&65,5\quad&\textrm{e}.&66,5 \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textbf{b}\\ &\begin{aligned} &\begin{array}{|c|c|c|c|}\hline \begin{aligned}&\textrm{Berat}\\ &\textrm{Badan} \end{aligned}&\color{red}\textrm{f}_{1}&\begin{aligned}&\textrm{Nilai Tengah}\\ &\qquad(\textrm{x}_{1}) \end{aligned}&\color{red}\textrm{f}_{1}\textrm{x}_{1}\\\hline 50-54&4&52&208\\ 55-59&6&57&342\\ 60-64&8&62&496\\ 65-69&10&67&670\\ 70-74&8&72&576\\ 75-79&4&77&308\\\hline &\sum \textrm{f}_{1}=\color{red}40&&\sum \textrm{f}_{1}\textrm{x}_{1}=\color{red}2600\\\hline \end{array}\\ &\textrm{maka nilai dari}\: \: \overline{\textrm{x}}\: \: \textrm{adalah}:\\ &\overline{\textrm{x}}=\displaystyle \frac{\sum \textrm{f}_{1}\textrm{x}_{1}}{\sum \textrm{f}_{1}}=\displaystyle \frac{2600}{40}=\color{red}65 \end{aligned}  \end{array}$.

$\begin{array}{ll} 48.&\textrm{Diketahui tabel distribusi frekuensi berikut}\\ &\begin{array}{|c|c|}\hline \textrm{Ukuran}&\textrm{Frekuensi}\\\hline 145-149&3\\ 150-154&5\\ 155-159&17\\ 160-164&15\\ 165-169&8\\ 170-174&2\\\hline \end{array}\\ &\textrm{Kuartil bawah dapat dinyatakan dengan}\: ....\\ &\begin{array}{lllllll}\\ \textrm{a}.&149,5+\left( \displaystyle \frac{12,5-3}{8} \right).5\\ \textrm{b}.&150+\left( \displaystyle \frac{12,5-3}{8} \right).5\\ \textrm{c}.&155+\left( \displaystyle \frac{12,5-8}{17} \right).5\\ \textrm{d}.&154,5+\left( \displaystyle \frac{12,5-8}{17} \right).5\\ \textrm{e}.&155,5+\left( \displaystyle \frac{12,5-8}{17} \right).5 \end{array}\\\\  &\textbf{Jawab}:\quad \color{red}\textrm{d}\\ &\begin{aligned}  &\textrm{Diketahui}\: n=\color{blue}50\\ &\textrm{Ditanyakan kuartil bawah, maka hal ini}\\ &=Q_{1}\: \Rightarrow \: x_{._{\frac{1}{4}n}}=x_{._{\frac{1}{4}50}}=x_{._{12,5}}\\ &\textrm{Perhatikan tabelnya lagi}\\ &\textrm{dengan penambahan warna berikut ini}\\ &\begin{array}{|c|c|}\hline \textrm{Ukuran}&\textrm{Frekuensi}\\\hline 145-149&\color{red}3\\ 150-154&\color{red}5\\ \color{blue}155-159&\color{blue}17\\ 160-164&15\\ 165-169&8\\ 170-174&2\\\hline \end{array}\\ &\textrm{maka nilai dari}\: \: Q_{1}\: \: \textrm{adalahh}:\\ &Q_{1}=L+\left( \displaystyle \frac{\frac{1}{4}n-f_{k}}{f} \right).c\\ &Q_{1}=\color{red}154,5+\left( \displaystyle \frac{12,5-8}{17} \right).5 ​\end{aligned} \end{array}$.

$\begin{array}{ll} 49.&\textrm{Diketahui tabel distribusi frekuensi berikut}\\ &\begin{array}{|c|c|}\hline \textrm{Ukuran}&\textrm{Frekuensi}\\\hline 5-9&2\\ 10-14&8\\ 15-19&10\\ 20-24&7\\ 25-29&3\\\hline \end{array}\\ &\textrm{Median dari tabel di atas adalah}\: ....\\ &\begin{array}{lllllll}\\ \textrm{a}.&15,0&&&\textrm{d}.&16,5\\ \textrm{b}.&15,5\quad&\textrm{c}.&16,0\quad&\textrm{e}.&17,0 \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{e}\\ &\begin{aligned}  &\textrm{Diketahui}\: n=\color{blue}30\\ &\textrm{Ditanyakan median, maka formulanya}\\ &=Q_{2}\: \Rightarrow \: x_{._{\frac{2}{4}n}}=x_{._{\frac{1}{2}.30}}=x_{._{15}}\\ &\textrm{Perhatikan tabelnya lagi}\\ &\textrm{dengan penambahan warna berikut ini}\\ &\begin{array}{|c|c|}\hline \textrm{Ukuran}&\textrm{Frekuensi}\\\hline 5-9&\color{red}2\\ 10-14&\color{red}8\\ \color{blue}15-19&\color{blue}10\\ 20-24&7\\ 25-29&3\\\hline \end{array}\\ &\textrm{maka nilai dari}\: \: Q_{2}\: \: \textrm{adalah}:\\ &Q_{2}=L+\left( \displaystyle \frac{\frac{2}{4}n-f_{k}}{f} \right).c\\ &Q_{1}=\color{red}14,5+\left( \displaystyle \frac{15-10}{10} \right).5\\ &\quad\: \: =14,5+\frac{25}{10}=14,5+2,5=\color{red}17,0 \end{aligned}  \end{array}$.

$\begin{array}{ll} 50.&\textrm{Jangkauan antarkuartil dari data}\\ &\textrm{berikut}:\\ &36\: \: 25\: \: 56\: \: 40\: \: 55\: \: 42\: \: 43\: \: 64\\ &82\: \: 70\: \: 28\: \: 35\: \: 38\: \: 45\: \: 54\\ &\textrm{adalah}\: ....\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{20}&&&\textrm{d}.&\textrm{5}\\ \textrm{b}.&\textrm{10}\quad &\textrm{c}.&\textrm{8}\quad&\textrm{e}.&\textrm{3} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{a}\\ &\begin{aligned} &\color{red}\textrm{Data mula-mula}\: \: \color{black}n=15\\ &36\: \: 25\: \: 56\: \: 40\: \: 55\: \: 42\: \: 43\: \: 64\\ &82\: \: 70\: \: 28\: \: 35\: \: 38\: \: 45\: \: 54\\ &\color{blue}\textrm{data durutkan}\\ &25\: \: 28\: \: 35\: \: 36\: \: 38\: \: 40\: \: 42\: \: 43\\ &45\: \: 54\: \: 55\: \: 56\: \: 64\: \: 70\: \: 82\\ &\textrm{Jangkauan antarkuartil adalah}\: H,\\ &H= Q_{3}-Q_{1} \\ &\quad\: =x_{._{\frac{3}{4}(n+1)}}-x_{._{\frac{1}{4}(n+1)}}\\ &\quad\: =x_{._{\frac{3}{4}(15+1)}}-x_{._{\frac{1}{4}(15+1)}}\\ &\quad\: =\left ( x_{._{12}}-x_{._{4}} \right )\\ &\quad\: =56-36\\ &\textrm{Jadi},\: H=Q_{3}-Q_{1}=\color{red}20 \end{aligned} \end{array}$.