Question

The table below shows the daily expenditure on food of 30 households in a locality:

Daily expenditure (in Rs)	Number of households
100 – 150	6
150 – 200	7
200 – 250	12
250 – 300	3
300 – 350	2

Find the mean and median daily expenditure on food.

 

Answer 1

We have the following:

Daily expenditure (in Rs)	Mid value `(x_i)`	Frequency `(f_i)`	Cumulative frequency	`(f_i × x_i)`
100 – 150	125	6	6	750
150 – 200	175	7	13	1225
200 – 250	225	12	25	2700
250 – 300	275	3	28	825
300 – 350	325	2	30	650
		`Ʃ f_i = 30`		`Ʃ f_i × x_i = 6150`

Mean, x = `(Ʃ_i  f_i × x_i)/(Ʃ_i f_i)`

              =`6150/30`

              =205

    Now, N = 30 

⇒`N/2 = 15`

The cumulative frequency just greater than 15 is 25 and the corresponding class is 200 – 250.
Thus, the median class is 200 – 250.
∴ l = 200, h = 50, f = 12, c = cf of preceding class = 13 and `N/2 = 15`

Now,
Median,` M_e = l + {h× ((N/2−c)/f)}`
                  `= 200 + {50 × ((15−13)/12)}`
                  `= (200 + 50 × 2/12)`
                   = 200 + 8.33
                    = 208.33