Find the mean of each of the following frequency distributions:
Class interval:
0−8
8−16
16−24
24−32
32−40
Frequency:
6
7
10
8
9
Answers
STEP DEVIATION METHOD:
Step deviation method is used in the cases where the deviation from the assumed mean 'A' are multiples of a common number. If the values of ‘di’ for each class is a multiple of ‘h’ the calculation become simpler by taking ui= di/h = (xi - A )/h
Here, h is the class size of each class interval.
★★ Find the class marks of class interval. These class marks would serve as the representative of whole class and are represented by xi.
★★ Class marks (xi) = ( lower limit + upper limit) /2
★★ We may take Assumed mean 'A’ to be that xi which lies in the middle of x1 ,x2 …..xn
MEAN = A + h ×(Σfiui /Σfi) , where ui = (xi - A )/h
[‘Σ’ Sigma means ‘summation’ ]
FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT
From the table : Σfiui = 7 , Σfi = 40
Let the assumed mean, A = 20, h = 8
MEAN = A + h ×(Σfiui /Σfi)
MEAN = 20 + 8 (7/40)
= 20 + 7/5
= 20 + 1.4
Mean = 21.4
Hence, the mean is 21.4
HOPE THIS ANSWER WILL HELP YOU….
_____Here's your Answer ________
Fiui = 7.
fi = 40.
Now,
Mean = A + h × ( fiui/fi)
=> 20 + 8 × ( 7/4)
=> 20 + 7/5
=> (100 + 7)/5
=> 107/5
=> 21.4
Therefore, Mean is 21.4.
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