Question

Find the mean of each of the following frequency distributions :
Class interval:
0−8
8−16
16−24
24−32
32−40
Frequency:
5
9
10
8
8

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 = 5 , Σfi = 40

Let the assumed mean, A = 20,  h = 8

MEAN = A + h ×(Σfiui /Σfi)

MEAN = 20  + 8(5/40)

= 20 + 5/5

= 20 + 1

= 21

Mean = 21

Hence, the mean is 21.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\bf \huge{Answer}$

Let the assumed mean data ( A ) = 20

After calculating data,

See the attachment,

We have,

A = 20

h = 8

Mean= ( a + h ) / N

= 20 + 8 / ( 5/40 )

= 20 + 1

$\sf{\huge{= 21 }}$

Hence,

$\underline{ \tt{The \: mean \: of \: distribution \: is \: 21.}}$

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