Find the arithmetic mean of each of the following frequency distr… - Vidyadip

Question

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

Class	$500-520$	$520-540$	$540-560$	$560-580$	$580-600$	$600-620$
Frequency	$14$	$9$	$5$	$4$	$3$	$5$

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Answer

Age	Frequency $f_i$	Mid-value $x_i$	$\text{u}_\text{i}=\frac{\text{x}_\text{i}-\text{550}}{\text{20}}$	$(f_i× u_i)$
$500-520$	$14$	$510$	$-2$	$-27$
$520-540$	$9$	$530$	$-1$	$-9$
$540-560$	$5$	$550 = A$	$0$	$0$
$560-580$	$4$	$570$	$1$	$4$
$580-600$	$3$	$590$	$2$	$6$
$600-620$	$5$	$610$	$3$	$15$
	$\sum\text{f}_\text{i}=40$			$\sum\text{f}_\text{i}\text{u}_\text{i}=-12$

Thus, $\text{A}=550,\ \text{h}=20$ and $\sum\text{f}_\text{i}=40,\ \sum\text{f}_\text{i}\text{u}_\text{i}=-12$
$\therefore$ Mean $\bar{\text{x}}=\text{A}+\Big[\text{h}\times\frac{\sum\text{(f}_\text{i}\times\text{u}_\text{i})}{\sum\text{f}_\text{i}}\Big]$
$550+\Big(\frac{-12}{40}\Big)$
$=500-6=544$

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