The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.
Expenditure (in rupees) (x) Frequency (fi) Expenditure (in rupees) (xi) Frequency (fi)
100 – 150 24 300 – 350 30
150 – 200 40 350 – 400 22
200 – 250 33 400 – 450 16
250 – 300 28 450 – 500 7
Find the average expenditure (in rupees) per household
Answers
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
FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT
From the table : Σfiui = - 35 , Σfi = 200, h = 50
Let the assumed mean, A = 275
MEAN = A + h ×(Σfiui /Σfi)
MEAN = 275 + 50 (-35/200)
= 275 - 1750/200
= 275 - 35/4
= 275 - 8.75
= 266.25
Hence, the average expenditure per household is ₹ 266.25 .
HOPE THIS ANSWER WILL HELP YOU….
Answer:
For mcq's answer is 266.5