Step Deviation Method (Mean)
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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.
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Solution:
Let the assumed mean be A = 20 and h = 5.
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N = Σ fi = 322 | |
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 | |
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Number of workers | |
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Solution :
Class intervals | Mid values (xi) | Frequency (fi) | di = xi - 25 | ui = (xi - 25) / 10 | fi ui |
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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.
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