Question

Take mean of the following distribution is 50. Find the value of x.
Class Interval 0-20 20-40 40-60 60-80 80-100
Frequency 34 3x-4 64 48 2(x-1)

Answer 1

Answer:

Class−intervals Class−mark

x

i

Frequency

f

i

f

i

x

i

0−20 10 17 170

20−40 30 p 30p

40−60 50 32 1600

60−80 70 q 70q

80−100 90 19 1710

∑f

i

=68+p+q ∑f

i

x

i

=3480+30p+70q

⇒ ∑f

i

=120 [ Given ]

⇒ ∑f

i

=68+p+q

∴ 68+p+q=120

⇒ p=52−q ------- ( 1 )

Mean=

∑f

i

∑f

i

x

i

50=

120

3480+30p+70q

6000=3480+30p+70q

2520=30(52−q)+70q [ From ( 1 ) ]

2520=1560−30q+70q

960=40q

∴ q=24

Substituting value of q=24 in equation ( 1 ) we get,

∴ p=28