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 $x_i$	$\text{u}_\text{i}=\frac{\text{x}_\text{i}-\text{550}}{\text{20}}$	$(f_i \times u_i)$
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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