$\begin{array}{ll}\\ 16.&(\textbf{UN IPA 2014})\\ &\textrm{Kuartil atas dari data pada tabel berikut}\\ &\textrm{adalah}\: ....\\ &\begin{array}{|c|c|}\hline \textrm{Data}&f\\\hline 20-25&4\\\hline 26-31&6\\\hline 32-37&6\\\hline 38-43&10\\\hline 44-49&12\\\hline 50-55&8\\\hline 56-61&4\\\hline \end{array}\\ &\begin{array}{llll}\\ \color{red}\textrm{a}.&49,25\\ \textrm{b}.&48,75\\ \textrm{c}.&48,25\\ \textrm{d}.&47,75\\ \textrm{e}.&47,25 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\color{blue}\begin{aligned}&\textrm{Kuartil atas}=\color{black}Q_{3},\: \textrm{dengan}\: \: n=\sum f=50\\ &\textrm{Kita sertakan lagi tabel di atas berikut}\\ &\begin{array}{|c|c|}\hline \color{black}\textrm{Data}&\color{red}f\\\hline 20-25&4\\\hline 26-31&6\\\hline 32-37&6\\\hline 38-43&10\\\hline \colorbox{magenta}{44-49}&\colorbox{magenta}{12}\\\hline 50-55&8\\\hline 56-61&4\\\hline \end{array}\\ &Q_{3}=\textrm{Datum ke}-\left ( \displaystyle \frac{3n}{4} \right )=x_{\frac{3.50}{4}}=x_{37,5}\\ &\textrm{dan}\: \: x_{37,5}\: \: \textrm{terletak di kelas interval}\: \: 44-49\\ &Q_{3}=t_{b}+p\left ( \displaystyle \frac{\displaystyle \frac{3n}{4}-F}{f} \right )\\ &\: \: \: \, =43,5+6\left ( \displaystyle \frac{37,5-26}{12} \right )\\ &\: \: \: \, =43,5+\displaystyle \frac{11,5}{2}\\ &\: \: \: \, =49,5+5,75\\ &\: \: \: \, =\color{red}49,25 \end{aligned} \end{array}$
$\begin{array}{ll}\\ 17.&(\textbf{UN IPA 2014})\\ &\textrm{Perhatikanlah histrogram berikut}\\ & \end{array}$
$\begin{array}{ll}\\ 18.&\textrm{Median dari data}\\ &3,4,7,5,6,9,9,7,6, 5,8\\ &\textrm{adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&5\\ \color{red}\textrm{b}.&6\\ \textrm{c}.&7\\ \textrm{d}.&8\\ \textrm{e}.&9 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}\textrm{Diketah}&\textrm{ui data adalah ganjil}\\ \textrm{Median}&\: \textrm{ (datum tengah) data tunggal}:\\ \textrm{Data}&:\: \: \color{black}3,4,7,5,6,9,9,7,6, 5,8\\ \textrm{setel}&\textrm{ah diurutkan}\\ \textrm{Data}&:\: \: \color{red}3,4,5,5,6,6,7,7,8,9,9\\ \textrm{Data}&:\: \: \color{red}3,4,5,5,6,\color{blue}6,\color{red}7,7,8,9,9 \end{aligned}\end{array}$
$\begin{array}{ll}\\ 19.&\textrm{Dari data berikut yang memiliki}\\ &\textbf{mean}\: \: 7\displaystyle \frac{1}{2}\: \: \textrm{dan}\: \textbf{median}\: 7\: \textrm{adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&2,5,6,9,7,8,5,14,8,11\\ \textrm{b}.&6,3,7,8,6,4,11,8,9,8\\ \textrm{c}.&3,7,10,7,9,5,10,2,14,11\\ \textrm{d}.&4,1,6,12,8,11,4,5,8,2\\ \color{red}\textrm{e}.&2,3,4,3, 10,8,12,6,15,12 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{e}\\ &\begin{array}{|l|l|}\hline \textrm{Mean}&\overline{x}=\displaystyle \frac{75}{10}=7,5\\\hline \textrm{Median}&2,5,6,9,7,8,5,14,8,11\\\hline \quad \textrm{a}&\color{blue}2,5,5,6,\color{red}7,8,\color{blue}8,9,11,14\\\hline \textrm{Mean}&\overline{x}=\displaystyle \frac{70}{10}=7\\\hline \textrm{Median}&6,3,7,8,6,4,11,8,9,8\\\hline \quad \textrm{b}&\color{blue}3,4,6,6,\color{red}7,8,\color{blue}8,8,9,11\\\hline \textrm{Mean}&\overline{x}=\displaystyle \frac{78}{10}=7,8\\\hline \textrm{Median}&3,7,10,7,9,5,10,2,14,11\\\hline \quad \textrm{c}&\color{blue}2,3,5,7,\color{red}7,9,\color{blue}10,10,11,14\\\hline \textrm{Mean}&\overline{x}=\displaystyle \frac{61}{10}=6,1\\\hline \textrm{Median}&4,1,6,12,8,11,4,5,8,2\\\hline \quad \textrm{d}&\color{blue}1,2,4,4,\color{red}5,6,\color{blue}8,8,11,12\\\hline \color{blue}\textrm{Mean}&\overline{x}=\displaystyle \frac{75}{10}=7,5\\\hline \color{blue}\textrm{Median}&2,3,4,3, 10,8,12,6,15,12\\\hline \quad \color{red}\textrm{e}&\color{blue}2,3,3,4,\color{red}6,8,\color{blue}10,12,12,15\\\hline \end{array} \end{array}$
$\begin{array}{ll}\\ 20.&\textrm{Berikut adalah daftar nilai matematika}\\ &\textrm{kelas XII IA1}\\ &\begin{array}{|l|c|c|c|c|c|c|c|c|}\hline \textrm{Nilai}&3&4&5&6&7&8&9&10\\\hline \textrm{Frekuensi}&3&5&5&9&8&6&2&2\\\hline \end{array}\\ &\textrm{Jika siswa yang nilainya di atas rata-rata}\\ &\textrm{akan diikutsertakan dalam seleksi}\\ &\textrm{olimpiade matematika, maka banyak}\\ & \textrm{siswa yang mengikuti seleksi olimpiade}\\ &\textrm{adalah}\: ...\: \textrm{siswa}\\ &\begin{array}{llll}\\ \textrm{a}.&6\\ \textrm{b}.&8\\ \textrm{c}.&10\\ \color{red}\textrm{d}.&18\\ \textrm{e}.&27 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\begin{aligned}&\begin{array}{|l|c|c|c|c|c|c|c|c|}\hline x_{i}&3&4&5&6&7&8&9&10\\\hline f_{i}&3&5&5&9&8&6&2&2\\\hline x_{i}f_{i}&9&20&25&54&56&48&18&20\\\hline \end{array}\\ &\color{blue}\textrm{Rata-rata nilai matematikanya}\\ &\color{magenta}\overline{x}=\displaystyle \frac{\sum x_{i}f_{i}}{\sum f_{i}}\\ &=\displaystyle \frac{250}{40}=6,25\\ &\color{blue}\textrm{Jadi, nilai rata-ratanya}\: \: \color{red}6,25\\ &\textrm{Sehingga yang bisa ikut selesksi adalah}\\ &\textrm{nilai di atas rata-rata yaitu}:7,8,9,10\\ &\textrm{dan totalnya yang mendapatkan nilai}\\ &\textrm{itu sebanyak}:\: \color{blue}8+6+2+2=\color{red}18\: \: \color{black}\textrm{siswa} \end{aligned} \end{array}$
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