Question

The weekly observations on cost of living index in a certain city for the year 2004-2005 are given below. Compute the weekly cost of living index.
Cost of living index:
1400-1500
1500-1600
1600-1700
Number of students:
5
10
20
Cost of living index:
1700-1800
1800-1900
1900-2000
Number of students:
9
6
2

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 = 7 ,  Σfi = 52

Let the assumed mean, A = 1650,  h = 100

MEAN = A + h ×(Σfiui /Σfi)

MEAN = 1650 + 100 (7 /52)

= 1650 + 700/52

= 1650 + 350/26

= 1650 + 13.46

= 1663.46

Mean = 1663.46

Hence, the mean is 1663.46

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\bf \huge{Answer :}$

$\sf \underline{Let \: the \: assumed \: mean ( A ) = 1650}$

We have,

A = 16

h = 100

$\sf{Mean = a \: + \: h ( sum/N )}$

= 1650 + 100 ( 7/52 )

= 1650 + ( 175/13 )

= 21625 / 13

$\tt{= 1663.46}$

Hence,

Weekly cost of the living index is 1663.46 Rs.

________________________ ❤️

Hope it helps !