Contoh Soal 2 Statistika

$\begin{array}{ll}\\ 6.&\textrm{Tabel berikut adalah nilai tes matematika}\\ &\qquad\qquad \begin{array}{|c|c|}\hline \textrm{Nilai}&f\\\hline 21-30&1\\\hline 31-40&2\\\hline 41-50&5\\\hline 51-60&7\\\hline 61-70&8\\\hline 71-80&8\\\hline 81-90&6\\\hline 91-100&1\\\hline \end{array}\\ &\textrm{Banyak siswa yang mendapatkan nilai 71}\\ &\textrm{atau lebih adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&16\\ \color{red}\textrm{b}.&15\\ \textrm{c}.&12\\ \textrm{d}.&12\\ \textrm{e}.&10 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{purple}\begin{aligned}&\textrm{Perhatikan kembali tabelnya}\\ &\qquad\qquad \color{black}\begin{array}{|c|c|}\hline \textrm{Nilai}&f\\\hline 21-30&1\\\hline 31-40&2\\\hline 41-50&5\\\hline 51-60&7\\\hline 61-70&8\\\hline \color{blue}71-80&\color{red}8\\\hline \color{blue}81-90&\color{red}6\\\hline \color{blue}91-100&\color{red}1\\\hline \end{array}\\ &\textrm{Nilai yang lebih dari 71 adalah}:\\ &\color{blue}8+6+1=17 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 7.&\textrm{Jangkauan dari tabel distribusi}\\ &\textrm{frekuensi pada no.6 di atas adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&60\\ \color{red}\textrm{b}.&70\\ \textrm{c}.&79\\ \textrm{d}.&89\\ \textrm{e}.&100 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{purple}\begin{aligned}&\textrm{Karena data berkelompok, maka}\\ &\textrm{Jangkauan}=\left ( \textrm{Nilai tengah kelas tertinggi} \right )\\ &\qquad\quad - \left ( \textrm{Nilai tengah kelas pertama} \right )\\ &=\displaystyle \frac{1}{2}\left ( (100+91)-(30+21) \right )=70 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 8.&\textrm{Jika}\: \: n=\textrm{banyak data},\: k=\textrm{banyak interval}\\ &\textrm{kelas, maka menurut aturan Sturges, rumus}\\ &\textrm{untuk menentukan nilai}\: \: k\: \: \textrm{adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&k=\log \left (10.n^{3,3} \right )\\ \color{red}\textrm{b}.&k=1+3,3\log n\\ \textrm{c}.&k=1-3,3\log (n-1)\\ \textrm{d}.&k=\log \left ( 10^{3,3}.n \right )\\ \textrm{e}.&k=\log n^{3,3}+2 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}&\textrm{Cukup jelas} \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 9.&\textrm{Rata-rata data soal no.6}\\ &\textrm{di atas adalah}\: ....\\ &\begin{array}{ll}\\ \color{red}\textrm{a}&\displaystyle 64,45\\ \textrm{b}&\displaystyle 64,55\\ \textrm{c}&\displaystyle 65,45\\ \textrm{d}&\displaystyle 65,55\\ \textrm{e}&\displaystyle 66\\ \end{array} \\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\color{blue}\begin{aligned}&\begin{array}{|c|c|c|c|}\hline \color{black}\textrm{Nilai}&\color{black}x_{i}&\color{red}f_{i}&\color{black}x_{i}.f_{i}\\\hline 21-30&25,5&1&25,5\\\hline 31-40&35,5&2&71\\\hline 41-50&45,5&5&227,5\\\hline 51-60&55,5&7&388,5\\\hline 61-70&65,5&8&524\\\hline 71-80&75,5&8&604\\\hline 81-90&85,5&6&513\\\hline 91-100&95,5&1&95,5\\\hline &\color{black}\sum_{i=1}^{8}&\color{red}38&\color{black}2449\\\hline \end{array}\\ &\textrm{Sehingga, rata-rata data nilai di atas adalah}\\ &\overline{x}=\displaystyle \frac{\sum x_{i}f_{i}}{\sum f_{i}}=\frac{2449}{38}=64,447368421\approx 64,45 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 10.&\textrm{Rumus untuk menentukan}\: \: \%f_{\textrm{rel}}=....\\ &\begin{array}{ll}\\ \textrm{a}&\displaystyle \frac{f_{i}+1}{\sum f}\times 100\%\\ \textrm{b}&\displaystyle \frac{f_{i}-1}{\sum f}\times 100\%\\ \color{red}\textrm{c}&\displaystyle \frac{f_{i}}{\sum f}\times 100\%\\ \textrm{d}&\displaystyle \frac{f_{i}}{\sum f +1}\times 100\%\\ \textrm{e}&\displaystyle \frac{f_{i}}{\sum f -1}\times 100\%\\ \end{array} \\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}&\textrm{Cukup jelas} \end{aligned} \end{array}$