Question

Find the missing frequencies x and y.
13. The median of the following frequency distribution is 46 and the total frequency is 230 :
10-20
15,
70-80
60-70
50-80
40-50
20-30 | 30-40
25
18
y
30
Frequency
12
find the missing frequencies x and y.​

Answer 1

Answer:

Class interval Frequency C.F.

10 - 20 12 12

20 - 30 30 42

30 - 40 f

1

42+f

1

40 - 50 65 107+f

1

50 - 60 f

2

107+f

1

+f

2

60 - 70 25 132+f

1

+f

2

70 - 80 18 150+f

1

+f

2

Let the frequency of the class 30 - 40 be f

1

and that of the calss 50 - 60 be f

2

The total frequency is 229

12 + 30 + f

1

+ 65 + f

2

+ 25 + 18 = 229 ⇒f

1

+f

2

=79

It is given that median is 46 clearly 46 lies in the class 40 - 50. So 40 - 50 is the median class

∴l=40,h=10,f=65andC=42+f

1

,N=229

Median = l+

f

2

N

−C

×h⇒46=40+

65

2

229

−(42+f

1

)

×10⇒46=40+

13

145−2f

1

⇒6=

13

145−2f

1

→2f

1

=67⇒f

1

=33.5or34 Since f

1

+f

2

=79∴f

2

=45 Hence f

1

=34 and f

2

=45