Step Deviation Method (Mean)
Step Deviation : Sometimes, during the application of the shortcut 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  





Frequency  





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



































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  




Number of workers  




Solution :
Class intervals  Mid values (xi)  Frequency (fi)  di = xi  25  ui = (xi  25) / 10  fi ui 





























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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