Question

Find the mean of the following frequency distribution is 57.6 and the total number of observation is 50.

Answer 1

Class Interval	Frequency (f)	Mid point (x)	fx
0−20	7	10	70
20−40	f1​	30	30f1​
40−60	12	50	600
60−80	f2​	70	70f2​
80−100	8	90	720
100−120	5	110	550
Total	∑f = 32 + f1​ + f2​ = 50		∑fx = 30f1​ + 70f2​ + 1940

 ∑f = f₁​ + f₂​ + 32 = 50

⇒ f_1​ + f₂​ = 18        ..........(i)

Mean \(\bar x = \frac{\sum fx}{\sum f}\)

\(57.6 = \frac{30f_1 + 70f_2+1940}{50}\)

30f₁ ​+ 70f₂ ​+ 1940 = 2880

30f₁​ + 70f₂​ = 940

or 3f₁​ + 7f₂ ​= 94       .............(ii)

Solving (i) and (ii)

f₁​ = 8, f₂ ​= 10

Thus, the value of f₁​ is 8 and the value of f₂ ​is 10.

Answer 2

∴ The missing frequencies are f₁ = 8 and f₂ = 10.