Question

The table below shows the daily expenditure on food of 25 households 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

To find the class mark (x_i) for each interval, the following relation is used:

Let the assumed mean, a = 225

Class size, h = 50

= `u_i = (x_i - a)/h`

= `(x_i - 225)/50`

Taking 225 as the assumed mean (a), d_i, u_i, f_iu_i are calculated as follows.

Daily expenditure (in Rs)	fi	xi	di = xi − 225	`u_i=(x_i-225)/50`	fiui
100 − 150	4	125	− 100	− 2	− 8
150 − 200	5	175	− 50	− 1	− 5
200 − 250	12	225	0	0	0
250 − 300	2	275	50	1	2
300 − 350	2	325	100	2	4
Total	25				-7

From the table, we obtain:

`sumf_i = 25`

`sumf_iu_i = -7`

`"Mean " barx = a+ ((sumf_1u_i)/(sumf_i))xh`

= `225 + ((-7)/25)xx(50)`

= 225 − 14

= 211

Therefore, mean daily expenditure on food is Rs 211.