Contoh Soal 3 Statistika

$\begin{array}{l}\\ 11.& \text{Perhatikan tabel distribusi frekuensi}\\ & \text{berikut}\\ & \begin{array}{|cc|}\hline \text{Interval}& f\\ 2-6& 2\\ 7-11& 3\\ 12-16& 3\\ 17-21& 6\\ 22-26& 6\\ \hline\end{array}\\ & \text{Rata-ratanya adalah}....\\ & \begin{array}{l}\\ \text{a}.& 17,5\\ \text{b}.& 17\\ \text{c}.& 16,75\\ \text{d}.& 16,5\\ \text{e}.& 15,5\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}& \begin{array}{|cccc|}\hline \text{Interval}& x_i& f_i& x_i.f_i\\ 2-6& 4& 2& 8\\ 7-11& 9& 3& 27\\ 12-16& 14& 3& 42\\ 17-21& 19& 6& 114\\ 22-26& 24& 6& 144\\ & \sum _{i=1}^5& 20& 335\\ \hline\end{array}\\ & \text{maka rata-ratanya}\\ & \bar{x}={\displaystyle \frac{\sum x_i.f_i}{\sum f_i}=\frac{335}{20}=16,75}\end{array}\end{array}$

$\begin{array}{l}\\ 12.& \text{Perhatikan tabel distribusi frekuensi}\\ & \text{berikut}\\ & \begin{array}{|cc|}\hline \text{Interval}& f\\ 51-60& 5\\ 61-70& 7\\ 71-80& 14\\ 81-90& 8\\ 91-100& 6\\ \hline\end{array}\\ & \text{Rata-ratanya adalah}....\\ & \begin{array}{l}\\ \text{a}.& 75,50\\ \text{b}.& 76,25\\ \text{c}.& 76,50\\ \text{d}.& 78,25\\ \text{e}.& 80,50\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}& \begin{array}{|cccc|}\hline \text{Interval}& x_i& f_i& x_i.f_i\\ 51-60& 55,5& 5& 277,5\\ 61-70& 65,5& 7& 458,5\\ 71-80& 75,5& 14& 1057\\ 81-90& 85,5& 8& 684\\ 91-100& 95,5& 6& 573\\ & \sum _{i=1}^5& 40& 3050\\ \hline\end{array}\\ & \text{maka rata-ratanya}\\ & \bar{x}={\displaystyle \frac{\sum x_i.f_i}{\sum f_i}=\frac{3050}{40}=76,25}\end{array}\end{array}$

$\begin{array}{l}\\ 13.& \text{Perhatikan tabel distribusi frekuensi}\\ & \text{berikut(data sama dengan no.12 di atas)}\\ & \begin{array}{|cc|}\hline \text{Interval}& f\\ 51-60& 5\\ 61-70& 7\\ 71-80& 14\\ 81-90& 8\\ 91-100& 6\\ \hline\end{array}\\ & \text{Mediannya adalah}....\\ & \begin{array}{l}\\ \text{a}.& 75,50\\ \text{b}.& 76,20\\ \text{c}.& 76,21\\ \text{d}.& 77,22\\ \text{e}.& 78,23\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}& \text{Diketahui},n=\sum f=40,\text{Perhatikan tabel}\\ & \text{berikut ini}\\ & \begin{array}{|cc|}\hline \text{Interval}& f_i\\ 51-60& 5\\ 61-70& 7\\ 71-80& 14\\ 81-90& 8\\ 91-100& 6\\ & 40\\ \hline\end{array}\\ & Q_k=\text{Datum ke}-\left({\displaystyle \frac{kn}{4}}\right)\\ & Median=Q_2=\text{Datum ke}-\left({\displaystyle \frac{2.40}{4}}\right)=x_{20}\\ & x_{20}\text{terletak pada kelas interval}:71-80\\ & \text{dengan}f=14,F\text{sebelum}{Q}_2=12,\\ & t_b=70,5,\text{serta}p=10\\ & \text{maka mediannya}\\ & Q_2=t_b+p\left({\displaystyle \frac{{\displaystyle \frac{2n}{4}-F}}{f}}\right)\\ & =70,5+10\left({\displaystyle \frac{20-12}{14}}\right)\\ & =70,5+5,714=76,21\end{array}\end{array}$

$\begin{array}{l}\\ 14.& \text{Perhatikan tabel distribusi frekuensi}\\ & \text{berikut}\\ & \begin{array}{|cc|}\hline \text{Skor}& f\\ 40-49& 8\\ 50-59& 9\\ 60-69& 22\\ 70-79& 15\\ 80-89& 6\\ \hline\end{array}\\ & \text{Modusnya adalah}....\\ & \begin{array}{l}\\ \text{a}.& 65,50\\ \text{b}.& 66,00\\ \text{c}.& 66,50\\ \text{d}.& 67,00\\ \text{e}.& 85,50\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}& \text{Diketahui}n=\sum f=60,modusnya\\ & \text{terdapat pada kelas dengan frekuensi terbanyak}\\ & \text{yaitu}:60-69,\text{dengan}p=10\\ & \{\begin{array}{ll}\mathrm{△}{f}_i& =f-f_1=22-9=13\\ \mathrm{△}{f}_{ii}& =f-f_2=22-15=7\end{array}\\ & \text{Sehingga}\\ & M_0=t_b+p\left({\displaystyle \frac{\mathrm{△}{f}_1}{\mathrm{△}{f}_1+\mathrm{△}{f}_2}}\right)\\ & M_0=59,5+10\left({\displaystyle \frac{22-9}{(22-9)+(22-15)}}\right)\\ & =59,5+{\displaystyle \frac{10.13}{13+7}}\\ & =59,5+6,5=66,0\end{array}\end{array}$

$\begin{array}{l}\\ 15.& (\mathbf{\text{UN 2013}})\\ & \text{Perhatikan tabel distribusi frekuensi}\\ & \text{berikut}\\ & \begin{array}{|cc|}\hline \text{Berat Badan (Kg)}& f\\ 45-49& 3\\ 50-54& 6\\ 55-59& 10\\ 60-64& 12\\ 65-69& 15\\ 70-74& 6\\ 75-79& 4\\ \hline\end{array}\\ & \text{Kuartil atasnya adalah}....\\ & \begin{array}{l}\\ \text{a}.& 66{\displaystyle \frac{5}{6}}\\ \text{b}.& 67{\displaystyle \frac{1}{6}}\\ \text{c}.& 67{\displaystyle \frac{5}{6}}\\ \text{d}.& 68{\displaystyle \frac{1}{6}}\\ \text{e}.& 68{\displaystyle \frac{4}{6}}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{d}}\\ & \begin{array}{rl}& \text{Kuartil atas}=Q_3,\text{dengan}n=\sum f=56\\ & Q_3=\text{Datum ke}-\left({\displaystyle \frac{3n}{4}}\right)=x_{\frac{3.56}{4}}=x_{42}\\ & \text{dan}{x}_{42}\text{terletak di kelas interval}65-69\\ & Q_3=t_b+p\left({\displaystyle \frac{{\displaystyle \frac{3n}{4}-F}}{f}}\right)\\ & =64,5+5\left({\displaystyle \frac{42-(3+6+10+12)}{15}}\right)\\ & =64{\displaystyle \frac{1}{2}+{\displaystyle \frac{11}{3}}}\\ & =64{\displaystyle \frac{3}{6}+3{\displaystyle \frac{4}{6}=68{\displaystyle \frac{1}{6}}}}\end{array}\end{array}$