Chapter 15 - Statistics

Example 4. The mean of the following frequency distribution is 62.8 and the sum of all frequency is 50. Complete the missing frequencies f₁ and f₂:

Class	0-20	20-40	40-60	60-80	80-100	100-120	Total
Frequency	5	f1	10	f2	7	8	50

Solution:-

Class	f1	x1	f1x1
0-20	5	10	50
20-40	f1	30	30f1
40-60	10	50	500
60-80	f2	70	70f2
80-100	7	90	630
100-120	8	110	880
	50		2060+ 30f1 + 70f2

5 + f₁ + 10 + f₂ + 7 + 8 = 50

30 + f₁ + f₂ = 50

f₁ + f₂ = 20

f₂ = 20 – f₁ ----------- (i)

2060 + 30f₁ + 70f₂ = 3140

30f₁ + 70f₂ = 3140 – 2060

30f₁ +70f₂ = 1080

3f₁ + 7f₂ = 108 ---------------- (ii)

3f₁ + 7(20 - f₁) = 108

-4f₁ + 140 = 108

-4f₁ = 108 - 140

-4f₁ = -32

f₁ = 8

From (i) f₂ = 20 – f₁

                 = 20 – 8

                 = 12