Question

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.

x	10	30	50	70	90
f	17	f1	32	f2	19	Total 120

Answer 1

x	f	fx
10	17	170
30	f1	30f1
50	32	1600
70	f2	70f2
90	19	1710
	N = 120	`sumfx=30f_1+70f_2+3480`

Given

Mean = 50

`(sumfx)/N=50`

`(30f_1+70f_2+3480)/120=50`

30f₁ + 70f₂ + 3480 = 6000         ............(i)

Also,

∑f = 120

17 + f₁ + 32 + f₂ + 19 = 120

f₁ + f₂ = 52

f₁ = 52 - f₂

Substituting value of f₁ in (i)

30(52 - f₂) + 70f₂ + 3480 = 6000

1560 - 30f₂ + 70f₂ + 3480 = 6000

40f₂ + 5040 = 6000

40f₂ = 6000 - 5040

40f₂ = 960

`f_2 = 960/40`

f₂ = 24

Hence

f₁ = 52 - f₂ = 52 - 24 = 28

∴ f₁ = 28, f₂ = 24