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)

$19$

$C.I$	$x_i$	$f_i$	$f_i{x}_i$	$(x_i-\overline{x}{)}^2$	$f_i(x_i-\overline{x}{)}^2$
$4-8$	$6$	$3$	$18$	$49$	$147$
$8-12$	$10$	$6$	$60$	$9$	$54$
$12-16$	$14$	$4$	$56$	$1$	$4$
$16-20$	$18$	$7$	$126$	$25$	$175$
		$\sum f_i=20$	$\sum f_i{x}_i=260$	$\sum (x_i-\overline{x}{)}^2=84$	$\sum f_i(x_i-\overline{x}{)}^2=380$

$\Rightarrow$ $\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{260}{20}=13$

$\Rightarrow$ $Variance\left({\sigma }^2\right)\frac{\sum f_i(x_i-\overline{x}{)}^2}{\sum f_i}=\frac{380}{20}=19$