Question

The mean of the following distribution is 62.8 and the sum of all the frequencies is 50. Find the missing frequencies f₁ and f₂.

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100	100 – 120
Frequency	5	f1	10	f2	7	8

Answer 1

Class	Freq (f)	Mid value	fx
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
Total	30 + f1 + f2		2060 + 30f1 + 70f2

Now, ∑f = 30 + f₁ + f₂ and ∑fx = 2060 + 30f₁ + 70f₂  ...(i)    

∑f = 50; mean = 62.8  ...(ii)  

From (i) 

30 + f₁ + f₂ = 50

f₁ + f₂ = 20  ...(iii) 

Using (i) and (ii) 

Mean = `(2060 + 30f_1 + 70f_2)/50` 

`62.8 = (2060 + 30f_1 + 70f_2)/50`

2060 + 30f₁ + 70f₂ = 62.8 × 50 

2060 + 30f₁ + 70f₂ = 3140 

30f₁ + 70f₂ = 1080 

3f₁ + 7f₂ = 108  ...(iv) 

From (iii) and (iv) 

f₁ = 8 

f₂ = 12