Question

From the following table compute arithmetic mean by direct method.

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
No. of students	$5$	$10$	$25$	$30$	$20$	$10$

Answer 1

Marks	Midpoint $\left(x\right)$	No. of students $\left(f\right)$	$fx$
$0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$	$5$ $15$ $25$ $35$ $45$ $55$	$5$ $10$ $25$ $30$ $20$ $10$	$25$ $150$ $625$ $1050$ $900$ $550$
		$\sum f=100$	$\sum f\left(x\right)=3300$

$\overline{x}=\frac{\sum f\left(x\right)}{\sum f}=\frac{3300}{100}=33$
$\therefore$ Mean $=33$