Calculate the mean,variance,and standard deviation for the following distribution:

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

(A) From the given data,we construct the following table:

Class	$f_i$	$x_i$	$f_ix_i$	$(x_i - \bar{x})^2$	$f_i(x_i - \bar{x})^2$
$30-40$	$3$	$35$	$105$	$729$	$2187$
$40-50$	$7$	$45$	$315$	$289$	$2023$
$50-60$	$12$	$55$	$660$	$49$	$588$
$60-70$	$15$	$65$	$975$	$9$	$135$
$70-80$	$8$	$75$	$600$	$49$	$392$
$80-90$	$3$	$85$	$255$	$529$	$1587$
$90-100$	$2$	$95$	$190$	$1089$	$2178$
Total	$N=50$	-	$3100$	-	$9090$

Mean $\bar{x} = \frac{\sum f_ix_i}{N} = \frac{3100}{50} = 62$.
Variance $(\sigma^2) = \frac{1}{N} \sum f_i(x_i - \bar{x})^2 = \frac{9090}{50} = 181.8$.
Standard deviation $(\sigma) = \sqrt{181.8} \approx 13.48$.