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 $=\frac{\sum f_i{x}_i}{\sum f_i}$
$=\frac{360}{20}=18$
$N=\sum _{i=1}^5{f}_i=20$,
$\sum _{i=1}^5{f}_i(x_i-\bar{x}{)}^2=340$
$\therefore$ Variance, ${\sigma }^2=\frac{1}{N}\cdot \sum f_i{\left(x_i-\bar{x}\right)}^2$
$=\left(\frac{1}{20}\times 340\right)=17$.