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 f 1 32 f 2 19 Total 120.

Question

Philoid · Accepted Answer

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

It is given that, mean = 50

= 50

3480 + 30f₁ + 70f₂ = 50 (120)

30f₁ + 70f₂ = 6000 – 3480

10 (3f₁ + 7f₂) = 10 (252)

3f₁ + 7f₂ = 252 (i) [Dividing by 10]

And N = 120

17 + f₁ + 32 + f₂ + 19 = 120

68 + f₁ + f₂ = 120

f₁ + f₂ = 52

Multiplying by ‘3’ on both sides, we get

3f₁ + 3f₂ = 156 (ii)

Subtracting (ii) from (i), we get

3f₁ + 7f₂ – 3f₁ – 3f₂ = 252 – 156

4f₂ = 96

f₂ =

= 24

Put value of f₂ in (i), we get

3f₁ + 7 * 24 = 252

3f₁ = 252 – 168

3f₁ = 84

f₁ =

= 28

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.x:1030507090f :17f132f219Total 120.

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.