Contoh Soal 3 Statistika

$\begin{array}{ll}\\ 11.&\textrm{Perhatikan tabel distribusi frekuensi}\\ &\textrm{berikut}\\ &\begin{array}{|c|c|}\hline \textrm{Interval}&f\\\hline 2-6&2\\\hline 7-11&3\\\hline 12-16&3\\\hline 17-21&6\\\hline 22-26&6\\\hline \end{array}\\ &\textrm{Rata-ratanya adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&17,5\\ \textrm{b}.&17\\ \color{red}\textrm{c}.&16,75\\ \textrm{d}.&16,5\\ \textrm{e}.&15,5 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}&\begin{array}{|c|c|c|c|}\hline \color{black}\textrm{Interval}&\color{black}x_{i}&\color{red}f_{i}&\color{black}x_{i}.f_{i}\\\hline 2-6&4&2&8\\\hline 7-11&9&3&27\\\hline 12-16&14&3&42\\\hline 17-21&19&6&114\\\hline 22-26&24&6&144\\\hline &\color{black}\sum_{i=1}^{5}&\color{red}20&\color{black}335\\\hline \end{array}\\ &\textrm{maka rata-ratanya}\\ &\overline{x}=\displaystyle \frac{\sum x_{i}.f_{i}}{\sum f_{i}}=\frac{335}{20}=16,75 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 12.&\textrm{Perhatikan tabel distribusi frekuensi}\\ &\textrm{berikut}\\ &\begin{array}{|c|c|}\hline \textrm{Interval}&f\\\hline 51-60&5\\\hline 61-70&7\\\hline 71-80&14\\\hline 81-90&8\\\hline 91-100&6\\\hline \end{array}\\ &\textrm{Rata-ratanya adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&75,50\\ \color{red}\textrm{b}.&76,25\\ \textrm{c}.&76,50\\ \textrm{d}.&78,25\\ \textrm{e}.&80,50 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}&\begin{array}{|c|c|c|c|}\hline \color{black}\textrm{Interval}&\color{black}x_{i}&\color{red}f_{i}&\color{black}x_{i}.f_{i}\\\hline 51-60&55,5&5&277,5\\\hline 61-70&65,5&7&458,5\\\hline 71-80&75,5&14&1057\\\hline 81-90&85,5&8&684\\\hline 91-100&95,5&6&573\\\hline &\color{black}\sum_{i=1}^{5}&\color{red}40&\color{black}3050\\\hline \end{array}\\ &\textrm{maka rata-ratanya}\\ &\overline{x}=\displaystyle \frac{\sum x_{i}.f_{i}}{\sum f_{i}}=\frac{3050}{40}=76,25 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 13.&\textrm{Perhatikan tabel distribusi frekuensi}\\ &\textrm{berikut(data sama dengan no.12 di atas)}\\ &\begin{array}{|c|c|}\hline \textrm{Interval}&f\\\hline 51-60&5\\\hline 61-70&7\\\hline 71-80&14\\\hline 81-90&8\\\hline 91-100&6\\\hline \end{array}\\ &\textrm{Mediannya adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&75,50\\ \textrm{b}.&76,20\\ \color{red}\textrm{c}.&76,21\\ \textrm{d}.&77,22\\ \textrm{e}.&78,23 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}&\textrm{Diketahui},\: n=\sum f=40,\: \: \textrm{Perhatikan tabel}\\ &\textrm{berikut ini}\\ &\begin{array}{|c|c|c|}\hline \color{black}\textrm{Interval}&\color{black}f_{i}\\\hline 51-60&\color{red}5\\\hline 61-70&\color{red}7\\\hline 71-80&14\\\hline 81-90&8\\\hline 91-100&6\\\hline &\color{red}40\\\hline \end{array}\\ &Q_{k}=\textrm{Datum ke}-\left ( \displaystyle \frac{kn}{4} \right )\\ &\color{red}Median=Q_{2}=\textrm{Datum ke}-\left ( \displaystyle \frac{2.40}{4} \right )=x_{20}\\ &x_{20}\: \: \textrm{terletak pada kelas interval}:\: \: 71-80\\ &\textrm{dengan}\: \: f=14,\: \: F\: \: \textrm{sebelum}\: \: Q_{2}=12,\\ &t_{b}=70,5,\: \: \textrm{serta}\: \: p=10\\ &\textrm{maka mediannya}\\ &Q_{2}=t_{b}+p\left ( \displaystyle \frac{\displaystyle \frac{2n}{4}-F}{f} \right )\\ &=70,5+10\left ( \displaystyle \frac{20-12}{14} \right )\\ &=70,5+5,714=76,21 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 14.&\textrm{Perhatikan tabel distribusi frekuensi}\\ &\textrm{berikut}\\ &\begin{array}{|c|c|}\hline \textrm{Skor}&f\\\hline 40-49&8\\\hline 50-59&9\\\hline 60-69&22\\\hline 70-79&15\\\hline 80-89&6\\\hline \end{array}\\ &\textrm{Modusnya adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&65,50\\ \color{red}\textrm{b}.&66,00\\ \textrm{c}.&66,50\\ \textrm{d}.&67,00\\ \textrm{e}.&85,50 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}&\textrm{Diketahui}\: \: n=\sum f=60,\: \:  \color{red}modusnya\\ &\textrm{terdapat pada kelas dengan frekuensi terbanyak}\\ & \textrm{yaitu}:\: 60-69,\: \: \textrm{dengan}\: \: p=10\\ &\begin{cases} \triangle f_{i} & =f-f_{1}=22-9=13 \\ \triangle f_{ii} & =f-f_{2}=22-15=7 \end{cases}\\ &\textrm{Sehingga}\\ &M_{0}=t_{b}+p\left ( \displaystyle \frac{\triangle f_{1}}{\triangle f_{1}+\triangle f_{2}} \right )\\ &M_{0}=59,5+10\left ( \displaystyle \frac{22-9}{(22-9)+(22-15)} \right )\\ &\: \: \: =59,5+\displaystyle \frac{10.13}{13+7}\\ &\: \: \: =\color{black}59,5+6,5=\color{red}66,0 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 15.&(\textbf{UN 2013})\\ &\textrm{Perhatikan tabel distribusi frekuensi}\\ &\textrm{berikut}\\ &\begin{array}{|c|c|}\hline \textrm{Berat Badan (Kg)}&f\\\hline 45-49&3\\\hline 50-54&6\\\hline 55-59&10\\\hline 60-64&12\\\hline 65-69&15\\\hline 70-74&6\\\hline 75-79&4\\\hline \end{array}\\ &\textrm{Kuartil atasnya adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&66\displaystyle \frac{5}{6}\\ \textrm{b}.&67\displaystyle \frac{1}{6}\\ \textrm{c}.&67\displaystyle \frac{5}{6}\\ \color{red}\textrm{d}.&68\displaystyle \frac{1}{6}\\ \textrm{e}.&68\displaystyle \frac{4}{6} \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\color{blue}\begin{aligned}&\textrm{Kuartil atas}=\color{black}Q_{3},\: \: \textrm{dengan}\: \: n=\sum f=56\\ &Q_{3}=\textrm{Datum ke}-\left ( \displaystyle \frac{3n}{4} \right )=x_{\frac{3.56}{4}}=x_{42}\\ &\textrm{dan}\: \: x_{42}\: \: \textrm{terletak di kelas interval}\: \: 65-69\\ &Q_{3}=t_{b}+p\left ( \displaystyle \frac{\displaystyle \frac{3n}{4}-F}{f} \right )\\ &\: \: \: =64,5+5\left ( \displaystyle \frac{42-(3+6+10+12)}{15} \right )\\ &\: \: \: =64\displaystyle \frac{1}{2}+\displaystyle \frac{11}{3}\\ &\: \: \: =\color{purple}64\displaystyle \frac{3}{6}+3\displaystyle \frac{4}{6}=\color{red}68\displaystyle \frac{1}{6} \end{aligned} \end{array}$