Question

how to find mean with the step deviation method

Answer 1

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.
variate51015202530Frequency204375677245
Solution: 
Let the assumed mean be A = 20 and h = 5.
Variate (xi)Frequency (fi)Deviation= di = xi - 20ui = (xi - 20 )/ 5fi ui520-15-3-601043-10-2-861575-5-1-75206700025725172304510290N = 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 interval0 - 1010 - 2020 - 3030 - 4040 - 50Number of workers71015810
Solution :
Class intervalsMid values (xi)Frequency (fi)di = xi - 25ui = (xi - 25) / 10fi ui0-1057-20-2-1410-201510-10-1-1020-30251500030-40358101840-50451020220N = Σ fi = 504
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.