Question

Find the mean of each of the following frequency distributions :
Class interval:
25−35
35−45
45−55
55−65
65−75
Frequency:
6
10
8
12
4

Answer 1

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 = -2, Σfi = 40

Let the assumed mean, A = 50,  h = 10

MEAN = A + h ×(Σfiui /Σfi)

MEAN = 50  + 10(-2 /40)

= 50 -  2/4

= 50 - 1/2

= 50 - 0.5

= 49.5  

Mean = 49.5  

Hence, the mean is 49.5  

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

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It is by direct method

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