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

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. [5 Marks]

CBSE 2023

Solution : 

Total Number of Families = 200
24+40+33+x+30+22+16+7=200
172+x=200
x=200-172
x=28

Median 

Monthly Expenditure (in ₹)	No. of Families (fi)	Cumulative Frequency (CF)
1000-1500	24	24
1500-2000	40	64
2000-2500	33	97
2500-3000	28	125
3000-3500	30	155
3500-4000	22	177
4000-4500	16	193
4500-5000	7	200
	Σfi=200

N=Σf_i=200
N/2 = 200/2 = 100
Median Class = 2500-3000
Lower Limit (L) = 2500
f =28
CF = 97

Class Size (h) = 3000-2500
= 500

Median = L+[(N/2-CF)/f]×h

= 2500+[(100-97)/28]×500
= 2500+(3/28)×500
= 2500+1500/28
= 2500+375/7
= 2500+53.571
= 2553.571
= ₹ 2553.57 

Hence, median monthly expenditure on milk is ₹ 2553.57

Mean

Monthly Expenditure (in ₹)	No. of Families (fi)	xi	di=xi-a	ui=di/h	fiui
1000-1500	24	1250	-1500	-3	-72
1500-2000	40	1750	-1000	-2	-80
2000-2500	33	2250	-500	-1	-33
2500-3000	28	2750 = a	0	0	0
3000-3500	30	3250	500	1	30
3500-4000	22	3750	1000	2	44
4000-4500	16	4250	1500	3	48
4500-5000	7	4750	2000	4	28
	Σfi=200				Σfiui =-35

Mean by Step Deviation Method 
a = 2750
h = 500
Mean (x̄) = a+[Σf_iu_i/Σf_i]×h
= 2750+[-35/200]×500
= 2750-175/2
= 2750-87.50
= 2662.50 ₹ 
Hence, mean monthly expenditure on milk is ₹ 2662.50.