calculate arithmetic mean from data using short cut and step deviation method
Answers
Answer:
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