Question

Weekly income of 600 families is tabulated below:

Weekly income (in Rs)	Number of families
0 – 1000	250
1000 – 2000	190
2000 – 3000	100
3000 – 4000	40
4000 – 5000	15
5000 – 6000	5
Total	600

Compute the median income.

Answer 1

Weekly income (in Rs)	Number of families `(bb(f_i))`	Cumulative frequency (cf)
0 – 1000	250	250
1000 – 2000	190	250 + 190 = 400
2000 – 3000	100	440 + 100 = 540
3000 – 4000	40	540 + 40 = 580
4000 – 5000	15	580 + 15 = 595
5000 – 6000	5	595 + 5 = 600

According to the question,

n = 600

∴ `n/2 = 600/2 = 300`

Cumulative frequency 440 lies in the interval 1000 – 2000.

Hence, lower median class, l = 1000

f = 190,

c_f = 250,

Class width, h = 1000

And total observation n = 600

∴ Median = `l + ((n/2 - cf))/f xx h`

= `1000 + ((300 - 250))/190 xx 1000`

= `1000 + 50/190 xx 1000`

= `1000 + 5000/9`

= 1000 + 263.15

= 1263.15

Hence, the median income is Rs.1263.15.