Statistika

1. Ukuran pemusatan

a. Mean

\(
\begin{aligned}
& \bar{x}=\frac{\Sigma\left(f_i \cdot x_i\right)}{\sum f_i} \\
& \bar{x}=\bar{x}_s+\frac{\sum\left(f_i \cdot d_i\right)}{\sum f_i} \\
& \bar{x}=\bar{x}_s+p \cdot \frac{\sum\left(f_i \cdot u_i\right)}{\sum f_i}
\end{aligned}
\)

b. Modus

Data yang sering muncul

\(
\begin{aligned}
M_o=L+p \cdot \frac{d_1}{d_1+d_2}
\end{aligned}
\)

c. Median

Nilai tengah data yang tersedia

\(
\begin{aligned}
M_e=L+p \cdot \frac{\left(\frac{n}{2}-F\right)}{f_{m e}}
\end{aligned}
\)

d. Kuartil

\(
\begin{aligned}
Q_i=L+p \cdot \frac{\left(\frac{1}{4} n-F\right)}{f_{Q_i}}
\end{aligned}
\)

2. Ukuran penyebaran

a. Jangkauan (J)

\(
\begin{aligned}
J=X_{\text {maks }}-X_{\text {min }}
\end{aligned}
\)

b. Jangkauan kuartil (JQ)

\(
\begin{aligned}
J Q=Q_3-Q_1
\end{aligned}
\)

c. Simpangan kuartil (SQ)

\(
\begin{aligned}
S Q=\frac{1}{2}\left(Q_3-Q_1\right)
\end{aligned}
\)

d. Simpangan rata-rata (SR)

\(
\begin{aligned}
& S R=\frac{\Sigma\left|x_i-\bar{x}\right|}{n} \\
& S R=\frac{\Sigma f_i\left|x_i-\bar{x}\right|}{\Sigma f_i}
\end{aligned}
\)

e. Ragam/varians \((R)\)

\(
\begin{aligned}
& R=S^2=\frac{\Sigma\left(x_i-\bar{x}\right)^2}{n} \\
& R=S^2=\frac{\Sigma f_i\left(x_i-\bar{x}\right)^2}{\Sigma f_i}
\end{aligned}
\)

f. Simpangan baku/deviasi standar (SB)

\(
\begin{aligned}
& S B=\sqrt{S^2}=\sqrt{\frac{\Sigma\left(x_i-\bar{x}\right)^2}{n}} \\
& S B=\sqrt{S^2}=\sqrt{\frac{\Sigma f_i\left(x_i-\bar{x}\right)^2}{\Sigma f_i}}
\end{aligned}
\)

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