Question

If the arithmetic mean of the data given below is 28, find the missing frequency?

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

Let the missing frequency be f₁

Arithmetic Mean = 28

Profit per Retail Shop (in Rs) Class Interval	No of Retail Shops (f)	Mid Value (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
	`sumf=80+f_1`		`sumfm=2100+35f_1`

`barX=(sumfm)/(sumf)`

or, `28=(2100+35f_1)/(80+f_1)`

or, 2240 + 28f₁ = 2100 + 35f₁

or, 2240 – 2100 = 35f₁ – 28f₁

or, 140 = 7f₁

f₁ = 20