Question

Find variance of the following data.

Class interval	Frequency
4-8	3
8-12	6
12-16	4
16-20	7

• A. $19$
• B. $20$
• C. $21$
• D. $23$

Answer 1

Answer: (A)

We have

Class Interval	Frequency $f_i$	Mid point $x_i$	$f_i{x}_i$	$x_i-\bar{x}$	$(x_i-\bar{x}{)}^2$	$f_i(x_i-\bar{x}{)}^2$
4-8	3	6	18	-7	49	147
8-12	6	10	60	-3	9	54
12-16	4	14	56	1	1	4
16-20	7	18	126	5	25	175
Total	20		260			380

$\therefore$ Mean $\left(\bar{x}\right)=\frac{\Sigma f_i{x}_i}{\Sigma f_i}$
$=\frac{260}{20}=13$
$\therefore$ Varience $\left({\sigma }^2\right)=\frac{\Sigma f_i{\left(x_i-\bar{x}\right)}^2}{\Sigma f_i}$
$=\frac{380}{20}=19$