Question

If the arithmetic mean of the data given below is 28, find (a) the missing frequency, and (b) the median of the series:

Profit per retail shop (in Rs)	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Number of retail shops	12	18	27	–	17	6

Answer 1

(i) Let the missing frequency be f₁

Arithmetic Mean = 28

Profit per Retail Shop (in Rs)	No of Retail Shops	Mid Value
Class Interval	(f)	(m)	fm
0 – 10	12	5	60
10 – 20	18	15	270
20 – 30	27	25	675
30 – 40	f1	35	35f1
40 – 50	17	45	765
50 – 60	6	55	330

or, 2240 + 28f₁ = 2100 + 35f₁

or, 2240 – 2100 = 35f₁ – 28f₁

or, 140 = 7f₁

f₁ = 20

(ii)

	Class Interval	Frequency (f)	Cumulative Frequency (CF)
	0 – 10	12	12
	10 – 20	18	30
	20 – 30	27	57
	30 – 40	20	77
	40 – 50	17	94
	50 – 60	6	100
	Total

So, the Median class = Size of item

= 50^th item

50^th item lies in the 57^th cumulative frequency and the corresponding class interval is 20 – 30.