Question

Find the mean of each of the following frequency distributions:
Class interval:
0-10
10-20
20-30
30-40
40-50
Frequency:
9
12
15
10
14

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 = 8   , Σfi = 60

Let the assumed mean, A = 25,  h = 10

MEAN = A + h ×(Σfiui /Σfi)

MEAN = 25  + 10(8/60)

= 25 + 8/6

= 25 + 4/3  

= 25 + 1.333

= 26.333

Mean = 26.333

Hence, the mean is 26.333

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

_______Heyy Buddy ❤_______

____Here's your Answer ______

A = 25

h = 10

fiui = 8

fi = 60

Now,

Mean = A + h × ( fiui / fi)

=> 25 + 10 × ( 8 / 60 )

=> 25 + 8/6

=> (150 + 8) / 6

=> 158 / 6

=> 26.33

Therefore,

Mean is 26.33
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