Find out the arithmetic mean using the step deviation method. Ite… - Vidyadip

Question

Find out the arithmetic mean using the step deviation method.

Item	Frequency
More than 0	28
More than 10	24
More than 20	14
More than 30	4

Hint: In the above problem, cumulative frequencies are given. Firstly, it will be changed into exclusive class interval and thereafter we will calculate arithmetic mean using the step deviation method.

✓

Answer

Calculation of Arithmetic Mean by Step Deviation Method
Items	Mid-Value (m)	Frequency (f)	dm(m - A) (A = 15)	$\text{d}'\text{m}\Big(\frac{\text{dm}}{\text{c}}\Big)$ (c = 10)	fd'm
0-10	5	28 - 24 = 4	-10	-1	-4
10-20	15	24 - 14 = 10	0	0	0
20-30	25	14 - 4 = 10	+10	+1	+10
30-40	35	4	+20	+2	+8
		$\Sigma\text{f}=28$			$\Sigma\text{f}\text{d}'\text{m}=+14$

$\therefore\ \overline{\text{X}}=\text{A}+\frac{\Sigma\text{fd}'\text{m}}{\Sigma\text{f}}\times\text{c}$
$=15+\frac{14}{28}\times10=15+5$
$\Rightarrow\ \overline{\text{X}}=20$

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