Question

Calculate the arithmetic mean by assumed mean method for the data given below.

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

Answer 1

Let the assumed mean be $A=35$

Marks	Mid-value $\left(x\right)$	No. of students $\left(f\right)$	$d=x-35$	$fd$
$0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$	$5$ $15$ $25$ $35$ $45$ $55$	$5$ $10$ $25$ $30$ $20$ $10$	$-30$ $-20$ $-10$ $0$ $10$ $20$	$-150$ $-200$ $-250$ $0$ $200$ $200$
		$\sum f=100$		$\sum fd=-200$

$\overline{x}=A+\frac{\sum fd}{\sum f}$
$=35+\left(\frac{-200}{100}\right)=35-2=33$