Contoh Soal 4 Statistika

$\begin{array}{l}\\ 16.& (\mathbf{\text{UN IPA 2014}})\\ & \text{Kuartil atas dari data pada tabel berikut}\\ & \text{adalah}....\\ & \begin{array}{|cc|}\hline \text{Data}& f\\ 20-25& 4\\ 26-31& 6\\ 32-37& 6\\ 38-43& 10\\ 44-49& 12\\ 50-55& 8\\ 56-61& 4\\ \hline\end{array}\\ & \begin{array}{l}\\ \text{a}.& 49,25\\ \text{b}.& 48,75\\ \text{c}.& 48,25\\ \text{d}.& 47,75\\ \text{e}.& 47,25\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{a}}\\ & \begin{array}{rl}& \text{Kuartil atas}=Q_3,\text{dengan}n=\sum f=50\\ & \text{Kita sertakan lagi tabel di atas berikut}\\ & \begin{array}{|cc|}\hline \text{Data}& f\\ 20-25& 4\\ 26-31& 6\\ 32-37& 6\\ 38-43& 10\\ \text{44-49}& \text{12}\\ 50-55& 8\\ 56-61& 4\\ \hline\end{array}\\ & Q_3=\text{Datum ke}-\left({\displaystyle \frac{3n}{4}}\right)=x_{\frac{3.50}{4}}=x_{37,5}\\ & \text{dan}{x}_{37,5}\text{terletak di kelas interval}44-49\\ & Q_3=t_b+p\left({\displaystyle \frac{{\displaystyle \frac{3n}{4}-F}}{f}}\right)\\ & =43,5+6\left({\displaystyle \frac{37,5-26}{12}}\right)\\ & =43,5+{\displaystyle \frac{11,5}{2}}\\ & =49,5+5,75\\ & =49,25\end{array}\end{array}$

$\begin{array}{l}\\ 17.& (\mathbf{\text{UN IPA 2014}})\\ & \text{Perhatikanlah histrogram berikut}\\ & \end{array}$

$.\begin{array}{l}\\ & \text{Modus dari data pada histogram adalah}....\\ & \begin{array}{l}\\ \text{a}.& 23,25\\ \text{b}.& 23,75\\ \text{c}.& 24,00\\ \text{d}.& 25,75\\ \text{e}.& 26,25\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}& \text{Diketahui dari data histogram di atas adalah}:\\ & \begin{array}{|cc|}\hline \text{Data}& f\\ 3-7& 4\\ 8-12& 6\\ 13-17& 8\\ 18-22& 10\\ \text{23-27}& \text{12}\\ 28-32& 6\\ 33-37& 4\\ 38-42& 2\\ \hline\end{array}\\ & \text{Saat menentukan batas interval kurang lebih sama}\\ & \text{seperti menentukan panjang interval kelas}\\ & \text{Modus dari histogram di atas}\\ & M_0=t_b+p\left({\displaystyle \frac{\mathrm{△}{f}_1}{\mathrm{△}{f}_1+\mathrm{△}{f}_2}}\right)\\ & =22,5+5\left({\displaystyle \frac{(12-10)}{(12-10)+(12-6)}}\right)\\ & =22,5+\left({\displaystyle \frac{2}{2+6}}\right)=22,5+{\displaystyle \frac{10}{8}}\\ & =22,5+1,25=23,75\end{array}\end{array}$.

$\begin{array}{l}\\ 18.& \text{Median dari data}\\ & 3,4,7,5,6,9,9,7,6,5,8\\ & \text{adalah}....\\ & \begin{array}{l}\\ \text{a}.& 5\\ \text{b}.& 6\\ \text{c}.& 7\\ \text{d}.& 8\\ \text{e}.& 9\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}\text{Diketah}& \text{ui data adalah ganjil}\\ \text{Median}& \text{ (datum tengah) data tunggal}:\\ \text{Data}& :3,4,7,5,6,9,9,7,6,5,8\\ \text{setel}& \text{ah diurutkan}\\ \text{Data}& :3,4,5,5,6,6,7,7,8,9,9\\ \text{Data}& :3,4,5,5,6,6,7,7,8,9,9\end{array}\end{array}$

$\begin{array}{l}\\ 19.& \text{Dari data berikut yang memiliki}\\ & \mathbf{\text{mean}}7{\displaystyle \frac{1}{2}\text{dan}\mathbf{\text{median}}7\text{adalah}....}\\ & \begin{array}{l}\\ \text{a}.& 2,5,6,9,7,8,5,14,8,11\\ \text{b}.& 6,3,7,8,6,4,11,8,9,8\\ \text{c}.& 3,7,10,7,9,5,10,2,14,11\\ \text{d}.& 4,1,6,12,8,11,4,5,8,2\\ \text{e}.& 2,3,4,3,10,8,12,6,15,12\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{|ll|}\hline \text{Mean}& \bar{x}={\displaystyle \frac{75}{10}=7,5}\\ \text{Median}& 2,5,6,9,7,8,5,14,8,11\\ \text{a}& 2,5,5,6,7,8,8,9,11,14\\ \text{Mean}& \bar{x}={\displaystyle \frac{70}{10}=7}\\ \text{Median}& 6,3,7,8,6,4,11,8,9,8\\ \text{b}& 3,4,6,6,7,8,8,8,9,11\\ \text{Mean}& \bar{x}={\displaystyle \frac{78}{10}=7,8}\\ \text{Median}& 3,7,10,7,9,5,10,2,14,11\\ \text{c}& 2,3,5,7,7,9,10,10,11,14\\ \text{Mean}& \bar{x}={\displaystyle \frac{61}{10}=6,1}\\ \text{Median}& 4,1,6,12,8,11,4,5,8,2\\ \text{d}& 1,2,4,4,5,6,8,8,11,12\\ \text{Mean}& \bar{x}={\displaystyle \frac{75}{10}=7,5}\\ \text{Median}& 2,3,4,3,10,8,12,6,15,12\\ \text{e}& 2,3,3,4,6,8,10,12,12,15\\ \hline\end{array}\end{array}$

$\begin{array}{l}\\ 20.& \text{Berikut adalah daftar nilai matematika}\\ & \text{kelas XII IA1}\\ & \begin{array}{|lcccccccc|}\hline \text{Nilai}& 3& 4& 5& 6& 7& 8& 9& 10\\ \text{Frekuensi}& 3& 5& 5& 9& 8& 6& 2& 2\\ \hline\end{array}\\ & \text{Jika siswa yang nilainya di atas rata-rata}\\ & \text{akan diikutsertakan dalam seleksi}\\ & \text{olimpiade matematika, maka banyak}\\ & \text{siswa yang mengikuti seleksi olimpiade}\\ & \text{adalah}...\text{siswa}\\ & \begin{array}{l}\\ \text{a}.& 6\\ \text{b}.& 8\\ \text{c}.& 10\\ \text{d}.& 18\\ \text{e}.& 27\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{d}}\\ & \begin{array}{rl}& \begin{array}{|lcccccccc|}\hline x_i& 3& 4& 5& 6& 7& 8& 9& 10\\ f_i& 3& 5& 5& 9& 8& 6& 2& 2\\ x_i{f}_i& 9& 20& 25& 54& 56& 48& 18& 20\\ \hline\end{array}\\ & \text{Rata-rata nilai matematikanya}\\ & \bar{x}={\displaystyle \frac{\sum x_i{f}_i}{\sum f_i}}\\ & ={\displaystyle \frac{250}{40}=6,25}\\ & \text{Jadi, nilai rata-ratanya}6,25\\ & \text{Sehingga yang bisa ikut selesksi adalah}\\ & \text{nilai di atas rata-rata yaitu}:7,8,9,10\\ & \text{dan totalnya yang mendapatkan nilai}\\ & \text{itu sebanyak}:8+6+2+2=18\text{siswa}\end{array}\end{array}$