Contoh Soal 2 Statistika

$\begin{array}{l}\\ 6.& \text{Tabel berikut adalah nilai tes matematika}\\ & \begin{array}{|cc|}\hline \text{Nilai}& f\\ 21-30& 1\\ 31-40& 2\\ 41-50& 5\\ 51-60& 7\\ 61-70& 8\\ 71-80& 8\\ 81-90& 6\\ 91-100& 1\\ \hline\end{array}\\ & \text{Banyak siswa yang mendapatkan nilai 71}\\ & \text{atau lebih adalah}....\\ & \begin{array}{l}\\ \text{a}.& 16\\ \text{b}.& 15\\ \text{c}.& 12\\ \text{d}.& 12\\ \text{e}.& 10\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}& \text{Perhatikan kembali tabelnya}\\ & \begin{array}{|cc|}\hline \text{Nilai}& f\\ 21-30& 1\\ 31-40& 2\\ 41-50& 5\\ 51-60& 7\\ 61-70& 8\\ 71-80& 8\\ 81-90& 6\\ 91-100& 1\\ \hline\end{array}\\ & \text{Nilai yang lebih dari 71 adalah}:\\ & 8+6+1=17\end{array}\end{array}$

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

$\begin{array}{l}\\ 8.& \text{Jika}n=\text{banyak data},k=\text{banyak interval}\\ & \text{kelas, maka menurut aturan Sturges, rumus}\\ & \text{untuk menentukan nilai}k\text{adalah}....\\ & \begin{array}{l}\\ \text{a}.& k=\log \left(10.n^{3,3}\right)\\ \text{b}.& k=1+3,3\log n\\ \text{c}.& k=1-3,3\log (n-1)\\ \text{d}.& k=\log ({10}^{3,3}.n)\\ \text{e}.& k=\log n^{3,3}+2\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}& \text{Cukup jelas}\end{array}\end{array}$.

$\begin{array}{l}\\ 9.& \text{Rata-rata data soal no.6}\\ & \text{di atas adalah}....\\ & \begin{array}{l}\\ \text{a}& {\displaystyle 64,45}\\ \text{b}& {\displaystyle 64,55}\\ \text{c}& {\displaystyle 65,45}\\ \text{d}& {\displaystyle 65,55}\\ \text{e}& {\displaystyle 66}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{a}}\\ & \begin{array}{rl}& \begin{array}{|cccc|}\hline \text{Nilai}& x_i& f_i& x_i.f_i\\ 21-30& 25,5& 1& 25,5\\ 31-40& 35,5& 2& 71\\ 41-50& 45,5& 5& 227,5\\ 51-60& 55,5& 7& 388,5\\ 61-70& 65,5& 8& 524\\ 71-80& 75,5& 8& 604\\ 81-90& 85,5& 6& 513\\ 91-100& 95,5& 1& 95,5\\ & \sum _{i=1}^8& 38& 2449\\ \hline\end{array}\\ & \text{Sehingga, rata-rata data nilai di atas adalah}\\ & \bar{x}={\displaystyle \frac{\sum x_i{f}_i}{\sum f_i}=\frac{2449}{38}=64,447368421\approx 64,45}\end{array}\end{array}$

$\begin{array}{l}\\ 10.& \text{Rumus untuk menentukan}\mathrm{\%}{f}_{\text{rel}}=....\\ & \begin{array}{l}\\ \text{a}& {\displaystyle \frac{f_i+1}{\sum f}\times 100\mathrm{\%}}\\ \text{b}& {\displaystyle \frac{f_i-1}{\sum f}\times 100\mathrm{\%}}\\ \text{c}& {\displaystyle \frac{f_i}{\sum f}\times 100\mathrm{\%}}\\ \text{d}& {\displaystyle \frac{f_i}{\sum f+1}\times 100\mathrm{\%}}\\ \text{e}& {\displaystyle \frac{f_i}{\sum f-1}\times 100\mathrm{\%}}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}& \text{Cukup jelas}\end{array}\end{array}$