Question

The monthly expenditure on milk in 200 families of a Housing Society is given below:

Monthly Expenditure (in ₹)	1000 – 1500	1500 – 2000	2000 – 2500	2500 – 3000	3000 – 3500	3500 – 4000	4000 – 4500	4500 – 5000
Number of families	24	40	33	x	30	22	16	7

Find the value of x and also, find the median and mean expenditure on milk.

The monthly expenditure on milk in 200 families of a Housing Society is given below:

Monthly Expenditure (in Rs.)	1000 - 1500	1500 - 2000	2000 - 2500	2500 - 3000	3000 - 3500	3500 - 4000	4000 - 4500	4500 - 5000
Number of families	24	40	33	x	30	22	16	7

Find the value of x and also find the mean expenditure.

Answer 1

Given, Total number of families = 200

∴ 24 + 40 + 33 + x + 30 + 22 + 16 + 7 = 200

`\implies` x = 200 – 172 = 28

Monthly expenditure (in ₹) (C.I.)	Number of families (fi)	Mid value (xi)	xifi	C.F.
1000 – 1500	24	1250	30,000	24
1500 – 2000	40	1750	70,000	64
2000 – 2500	33	2250	74,250	97
2500 – 3000	28	2750	77,000	125
3000 – 3500	30	3250	97,500	155
3500 – 4000	22	3750	82,500	177
4000 – 4500	16	4250	68,000	193
4500 – 5000	7	4750	33,250	200
	`bb(N = sumf_i = 200)`		`bb(sumx_i f_i = 5,32,500)`

Mean = `(sumx_i f_i)/(sumf_i)`

= `(5,32,500)/200`

= ₹ 2662.5

Now, `N/2` = `200/2` = 100^th

100^th observation lies in class 2500 – 3000, which is known as median class.

l = lower limit of median class = 2500

N = number of families = 200

f = frequency of median class = 28

C.F. = cumulative frequency of the class preceding the median class = 97

h = class size = 500

Median = `l + ((N/2 - C.F.))/f xx h`

Median = `2500 + ((200/2 - 97))/28 xx 500`

= `2500 + (100 - 97)/28 xx 500`

= `2500 + 3/7 xx 125`

= 2500 + 53.571

= 2553.571