Question

The table below shows the daily expenditure on food of 25 household in a locality
Daily expenditure (in Rs):
100−150
150−200
200−250
250−300
300−350
Number of households:
4
5
12
2
2
Find the mean daily expenditure on food by a suitable method.

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 = 25

Let the assumed mean, A = 225,  h = 50

MEAN = A + h ×(Σfiui /Σfi)

Mean = 225 + 50 (-7/25)

= 225 - 2×2

= 225 - 14

= 211

Mean = 211

Hence, the Mean daily expenditure on food is ₹ 211.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\small{\bold {REFER \: THE \: ATTACHMENT}}$