Question

In the following table, Σf = 200 and mean = 73. Find the missing frequencies f₁, and f₂.

x	0	50	100	150	200	250
f	46	f1	f2	25	10	5

Answer 1

We have,

x	f	fx
0	46	0
50	f1	50f1
100	f2	100f2
150	25	3750
200	10	2000
250	5	1250
	Σf = 86 + f1 + f2	Σfx = 7000 + 50f1 + 100f2

Given, Σf = 200

`=>` 86 + f₁ + f₂ = 200

`=>` f₁ + f₂ = 114    ...(i)

Mean = `(Σfx)/(Σf)`

`=> 73 = (7000 + 50f_1 + 100f_2)/200`

`=>` 7000 + 50f₁ + 100f₂ = 14600

`=>` 50f₁ + 100f₂ = 7600

`=>` f₁ + 2f₂ = 152   ...(ii)

Subtracting (ii) from (i), we get

f₂ = 38

`=>` f₁ = 114 – 38 = 76

Hence, f₁ = 76 and f₂ = 38