Question

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.
Find the average expenditure (in rupees) per household.
Expenditure Frequency Expenditure Frequency
(in rupees) (f) (in rupees) (f)
(in rupees) (X)
100-150 24 300-350 30
150-200 40 350-400 22
200-250 33 400-450 16
250-300 28 450-500 7

Answer 1

The average expenditure is Rs 266.25                                

Step-by-step explanation:

Step 1 :

The average expenditure can be computed as follows :

Finding the average of the data through assumed mean method

Find the class mark of the class intervals (x)

Choose any value from the class mark (A)

Subtract the value of A from the class marks (d)

Multiply the frequencies(f) with the corresponding values of d(fd)

Find the Sum of the frequencies

Find the sum of fd  

Then calculate the mean as

Mean =  A + Σfd ÷ Σf

Step 2 :

Calculations of the above steps

x         f           d(x-A,A=125)             fd

125     24         0                               0

175      40        50                            2000

225     33        100                         3300

275     28        150                          4200

325      30       200                       6000

375       22      250                         5500

425       16       300                          4800

475        7         350                         2450

Mean = 125 +  28250 ÷ 200

        =   125 + 141.25

        = 266.25

Step 3 :

Answer :

The average expenditure per household is Rs.266.25

                 

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