Question

Calculate the mean of the distribution given below using the short cut method.

Marks	$11-20$	$21-30$	$31-40$	$41-50$	$51-60$	$61-70$	$71-80$
No. of students	$2$	$6$	$10$	$12$	$9$	$7$	$4$

Answer 1

Marks (C.I.)	$f$	Mean Value $x$	$A=45.5$ $d=x-A$	$f\times d$
$11-20$	$2$	$15.5$	$-30$	$-60$
$21-30$	$6$	$25.5$	$-20$	$-120$
$31-40$	$10$	$35.5$	$-10$	$-100$
$41-50$	$12$	$45.5$	$0$	$0$
$51-60$	$9$	$55.5$	$10$	$90$
$61-70$	$7$	$65.5$	$20$	$140$
$71-80$	$4$	$75.5$	$30$	$120$
	$\sum f=50$			$\sum fd=70$

$\therefore$ Mean $=A+\frac{\sum fd}{\sum f}$
$=45.5+\frac{70}{50}=45.5+1.4$
$=46.9$