Question

The following table gives the distribution of total household expenditure ( in rupees) of manual workers in a city.

Expenditure: (in Rs.)	100-150	150-200	200-250	250-300	300-350	350-400	400-450	450-500
Frequency:	24	40	33	28	30	22	16	7

Find the average expenditure (in Rs.) per household.

Answer 1

Let the assumed mean be A= 325 and h= 50.
Calculation of Mean

Expenditure (in Rs.)$x_i$	Frequency $f_i$	Mid values $x_i$	$d_i=x_i-A=x_i-325$	$u_i=\frac{x-A}{h}=\frac{x_i-325}{50}$	$f_i{u}_i$
100-150	24	125	-200	-4	-96
150-200	40	175	-150	-3	-120
200-250	33	225	-100	-2	-66
250-300	28	275	-50	-1	-66
300-350	30	325	0	0	0
350-400	22	375	50	1	22
400-450	16	425	100	2	32
450-500	7	475	150	3	21
	$N=\sum f_i=200$				$\sum f_i{u}_i=-235$

We have,
N= 200, A= 325, h= 50, and $\sum f_i{u}_i=-235$
$\therefore \overline{X}=A+h\frac{1}{N}\sum f_i{u}_i$
$\Rightarrow \overline{X}=325=50\times \left[\frac{-235}{200}\right]$
$\Rightarrow \overline{X}=325-\frac{235}{4}=325-58.75=266.25$
Hence, the average expenditure is Rs. 266.25.