Question

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

Expenditure (in rupees ) ($x$)	Frequency ($f$)	Expenditure (in rupees) ($x_i)$	Frequency ($f_i$)
$100-150$	$24$	$300-350$	$30$
$150-200$	$40$	$350-400$	$22$
$200-250$	$33$	$400-450$	$16$
$250-300$	$28$	$450-500$	$7$

Find the average expenditure (in rupees) per household.

Answer 1

Class interval	x1	d1	u1	f1	f1u1
100-150	125	-150	-3	24	-12
150-200	175	-100	-2	40	-80
200-250	225	-50	-1	33	-33
250-300	275	0	0	28	0
300-350	325	50	1	30	30
350-400	375	100	2	22	44
400-450	425	150	3	16	48
450-500	475	200	4	7	28

$d_1=x_1-275$

$u_1=\frac{x_1-275}{50}$

Let the assumed mean be,

$A=275$

$h=50$

$mean=A+h\times \frac{\sum f_1{u}_1}{N}$

$=275+50\times \frac{-35}{200}$

$=266.25$