Step  Deviation Method (Mean)

Step Deviation : Sometimes, during the application of the short-cut method for finding the mean, the deviation d, are divisible by a common number ‘h’ .In this case the di = xi – A is reduced to a great extent as di becomes di / h. So the formula of mean by this is :

Where ui = ( xi – A) / h ; h = class width and N = Σ fi
Finding mean by using this formula is known as the Step Deviation Method.
Some solved examples
1) Apply Step - Deviation method to find arithmetic mean of the following frequency distribution.

variate	5	10	15	20	25	30
Frequency	20	43	75	67	72	45

Solution:
Let the assumed mean be A = 20 and h = 5.

Variate (xi)	Frequency (fi)	Deviation= di = xi - 20	ui = (xi - 20 )/ 5	fi ui
5	20	-15	-3	-60
10	43	-10	-2	-86
15	75	-5	-1	-75
20	67	0	0	0
25	72	5	1	72
30	45	10	2	90
	N = Σ fi = 322			-59

N = 322, A = 20 , h = 5 and Σ fi ui = - 59

⇒ Mean = 20 + 5 ( - 59 / 322)
⇒ Mean = 20 – 0.91
∴ Mean = 19.09
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2) Find the mean of following frequency distribution:

Class interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50
Number of workers	7	10	15	8	10

Solution :

Class intervals	Mid values (xi)	Frequency (fi)	di = xi - 25	ui = (xi - 25) / 10	fi ui
0-10	5	7	-20	-2	-14
10-20	15	10	-10	-1	-10
20-30	25	15	0	0	0
30-40	35	8	10	1	8
40-50	45	10	20	2	20
		N = Σ fi = 50			4

A = 25 , h = 10 , N = 50 and Σ fi ui = 4

⇒ Mean = 25 + 10 x ( 4 / 50)
⇒ Mean = 25 + 0.8
∴ Mean = 25.8

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• Direct method
• Short cut method
• Step - Deviation method.

From step deviation to measures of central tendency

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