Question

Find the mean of the following frequency distribution by the step deviation method:

Class	$100-110$	$110-120$	$120-130$	$130-140$	$140-150$
Frequency	$15$	$18$	$32$	$25$	$10$

Answer 1

Class	$x$	$f$	$t=\frac{x-A}{i}$	$f\times t$
$100-110$	$105$	$15$	$-2$	$-30$
$110-120$	$115$	$18$	$-1$	$-18$
$120-130$	$A=125$	$32$	$0$	$0$
$130-140$	$135$	$25$	$1$	$25$
$140-150$	$145$	$10$	$2$	$20$
		$\Sigma f=100$		$\Sigma ft=-3$

From the table $A=125\text{and}i=10$

Mean, $\overline{x}=A+\frac{\Sigma ft}{\Sigma f}\times i$

$\Rightarrow \overline{x}=125+\frac{-3}{100}\times 10$

$\Rightarrow \overline{x}=125-0.3$

$\Rightarrow \overline{x}=124.70$

Hence, the mean is $124.70$.