D. Persentil
$\begin{aligned}&\textrm{Dilambangkan dengan}\: \: P_{i}\\ &\textrm{dibaca: persentil ke}-i\\ &\color{red}\textrm{Rumus data tunggal}:\\ &\textbf{Dengan rumus pendekatan interpolasi linear}\\ &P_{i}=\textrm{datum ke}-\displaystyle \frac{i}{100}(n+1)\\ &\textrm{jika}\: \: \displaystyle \frac{i}{100}(n+1)\: \: \textrm{tidak bulat, gunakan rumus}\\ &\textrm{interpolasi linear, yaitu}:\\ &\qquad\quad P_{i}=x_{k}+d\left ( x_{k+1}-x_{k} \right )\\ &\textrm{dengan}\: \: d\: \: \textrm{adalah nilai desimalnya}\\ &\textbf{Dengan tanpa rumus interpolasi linear}\\ &\begin{array}{|c|c|}\hline n\: \: \textrm{ganjil}&n\: \: \textrm{genap}\\\hline P_{1}=x_{._{\frac{1}{100}(n+1)}}&P_{1}=\displaystyle \frac{1}{2}\left (x_{._{\frac{1}{100}n}}+x_{._{\frac{1}{100}n+1}} \right )\\ P_{2}=x_{._{\frac{2}{100}(n+1)}}&P_{2}=\displaystyle \frac{1}{2}\left (x_{._{\frac{2}{100}n}}+x_{._{\frac{2}{100}n+1}} \right )\\ \vdots &\vdots \\ P_{99}=x_{._{\frac{99}{100}(n+1)}}&P_{99}=\displaystyle \frac{1}{2}\left (x_{._{\frac{99}{100}n}}+x_{._{\frac{99}{100}n+1}} \right )\\\hline \end{array}\\ &\textrm{Catatan: sesuaikan dengan kondisi soal}\\ &\color{red}\textrm{Rumus data berkelompok/berfrekuensi}:\\ &P_{i}=L_{i}+\left ( \displaystyle \frac{\displaystyle \frac{i}{100}n-f_{k}}{f} \right )\times c\\ &\color{blue}\textrm{Penjelasan}\\ &\qquad \begin{aligned}D_{i}&=\textrm{persentil ke}-i\\ i&=1,2,3\\ L_{i}&=\textrm{tepi bawah kelas persentil ke}-i\\ f_{k}&=\textrm{frekuensi kumulatif sebelum}\\ &\quad\: \, \textrm{sebelum kelas persentil ke}-i\\ f&=\textrm{frekuensi kelas persentil ke}-i\\ c&=\textrm{panjang kelas interval}\\ n&=\textrm{banyak data/kelas interval} \end{aligned} \end{aligned}$.
Catatan :untuk bahasan interpolasi linear ada di sini
$\LARGE\colorbox{yellow}{CONTOH SOAL}$.
$\begin{array}{ll} 1.&\textrm{Tentukan persentil ke-29 dan ke-75 dari data berikut}\\ &4,7,5,6,6,7,8,4,9,5,2,3,6,4,8\\\\ &\textrm{Jawab}:\\ &\textrm{Banyak datum}=15\\ &\textbf{dengan rumus pendekatan interpolasi linear}\\ &\textrm{Data mula-mula}\\ &\quad :4,7,5,6,6,7,8,4,9,5,2,3,6,4,8\\ &\textrm{Data setelah diurutkan}\\ &\quad :2,3,4,4,4,5,5,6,6,6,7,7,8,8,9\\ &\begin{aligned}P_{29}&=\displaystyle \frac{29}{100}\left ( 15+1 \right )\\ &=\displaystyle \frac{464}{100}=4,64\\ &=x_{4}+0,64(x_{5}-x_{4})\\ &=4+0,64(5-5)=4+0=\color{red}4\\ P_{75}&=\displaystyle \frac{75}{100}\left ( 15+1 \right )\\ &=\displaystyle \frac{1200}{100}=12\\ &=x_{12}\\ &=\color{red}7\\ \end{aligned} \end{array}$.
$\begin{array}{ll}\\ 2.&\textrm{Persentil ke-32}\: \: \left ( P_{32} \right )\: \: \textrm{dari data berikut adalah}\: ....\\ &\begin{array}{|c|c|}\hline \textrm{Nilai}&f\\\hline 41-45&7\\ 46-50&12\\ 51-55&9\\ 56-60&8\\ 61-65&4\\\hline \end{array}\\ &\begin{array}{llll}\\ \color{red}\textrm{a}.&46\\ \textrm{b}.&47\\ \textrm{c}.&48\\ \textrm{d}.&51\\ \textrm{e}.&52 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\color{blue}\begin{aligned}\textrm{Diketahui}&\: \textrm{persentil ke}-32=\color{black}P_{32},\\ &\textrm{dengan}\: \: n=\sum f=40\\ P_{i}&=\color{black}L_{i}+c\left ( \displaystyle \frac{\displaystyle \frac{i\times n}{100}-f_{k}}{f} \right )\\ P_{32}&=\color{black} \textrm{datum ke}-\left ( \displaystyle \frac{32n}{100} \right )\\ &=x_{\frac{32\times 40}{100}}=\color{red}x_{12,8}\\ \textrm{Dan}\: \: \color{red}x_{12}\: \: &\textrm{terletak di kelas interval}\: :\: \color{red}46-50 \\ P_{32}&=\color{black}545,5+5\left ( \displaystyle \frac{12,8-7}{12} \right )\\ &=\color{black}45,5+0,48333...\\ &=\color{red}45.9833... \approx 46 \end{aligned} \end{array}$
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