Question

The mean of the following frequency
distribution is 50, but the frequencies fi and
f2 in classes 20-40 and 60-80, respectively
are not known. Find these frequencies,
if the sum of all the frequencies is 120.
Class
Frequency
0-20
17
20-40
fi
40-60
32
60-80
f2
80-100
19​

Answer 1

Answer:

mid value

(x

1

) frequency

(f

1

) f

i

x

i

0−20 10 17 170

20−40 30 f

1

30f

1

40−60 50 32 1600

60−80 70 f

2

70f

2

80−100 90 19 1710

68+f

1

+f

2

3480+30f

1

+70f

2

∑f

i

=120

∴ we have 120=68+f

1

+f

2

⇒f

1

+f

2

=52..........(1)

mean =

∑f

i

∑f

i

x

i

50=

120

3480++30f

i

+70f

2

30f

1

+70f

2

=6000−3460=2520

3f

1

+7f

2

=252..........(2)

eq(1)×7⇒7f

1

+7f

2

=7×52=364

(2)⇒3f

1

+7f

2

=252

− − −

4f

1

=112⇒f

1

=28

f

1

=28⇒from(1)

⇒f

2

=52−f

1

=52−28

f

2

=24