Find the mean of the following frequency distribution by the step… - Vidyadip

Question

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

$\text{Class}$	$100-110 $	$110-120 $	$120-130 $	$130-140 $	$140-150 $
$\text{Frequency}$	$15$	$18$	$32$	$25$	$10$

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Answer

$\text{Class Interval}$	$x_i$	$f_i$	$A = 35.5 d = x - A$	$f_id$
$100-110$	$105$	$15$	$-2$	$-30$
$110-120$	$115$	$18$	$-1$	$-18$
$210-130$	$A=125$	$32$	$ 0$	$0$
$310-140$	$135$	$25$	$1$	$25$
$140-150$	$145$	$10$	$2$	$20$
$\text{Total}$		$100$		$-3$

$ A =125 \text { and } h _{ i }=10$
$\bar{x}=A+ h \times \frac{\Sigma f_i u }{\Sigma f_i}$
$\bar{x}=125+10 \times \frac{-3}{100}$
$\bar{x}=125-0.3$
$\bar{x}=124.70$
$\therefore \text { Mean }=124.70$

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