Question

Calculate the variance and standard deviation of the following continuous frequency distribution

Class interval	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Frequency	$3$	$7$	$12$	$15$	$8$	$3$	$2$

Answer 1

Class Interval Mid Value $\left(x\right)$ frequency $\left(f\right)$ $fx$ $f{x}^2$

$30-40$ $35$ $3$ $105$ $3675$

$40-50$ $45$ $7$ $315$ $14175$

$50-60$ $55$ $12$ $660$ $36300$

$60-70$ $65$ $15$ $957$ $63375$

$70-80$ $75$ $8$ $600$ $45000$

$80-90$ $85$ $3$ $255$ $21675$

$90-100$ $95$ $2$ $190$ $18050$

$n=\sum f=50$

$\overline{x}=\frac{1}{n}\sum f{x}_i=\frac{3082}{50}=61.64$

Variance $\left({\sigma }^2\right)=\frac{1}{n}\sum f{x}^2-(\overline{x}{)}^2=\frac{202250}{50}-(61.64{)}^2=245.5104$

Standard deviation $\left(\sigma \right)=\sqrt{245.5104}=15.67$