# 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

Direct method
Short cut method
Step - Deviation method.

From step deviation to measures of central tendency

Statistics

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