Question

The frequency distribution table is given here.

$x_i$	$10$	$15$	$18$	$20$	$25$
$f_i$	$3$	$2$	$5$	$8$	$2$

Find the variance.

• A. $19$
• B. $17$
• C. $18$
• D. $16$

Answer 1

Answer: (B)

$\bar{x}=$ Mean $=\frac{\sum f_{i}x_{i}}{\sum f_{i}}$
$=\frac{360}{20}=18$
$N=\displaystyle \sum_{i=1}^5 f_i=20$,
$\displaystyle \sum_{i=1}^5 f_i(x_i-\bar{x})^2=340$
$\therefore $ Variance, $\sigma^{2}=\frac{1}{N}\cdot\sum f_{i}\left(x_{i}-\bar{x}\right)^{2}$
$=\left(\frac{1}{20}\times340\right)=17$.