Question

if the median of the following data is 32.5 find the missing frequencies . C.I = 10-20, 20-30 , 30-40,40-50,50-60,60-70 . frequency = 3,x,9,12,y,3,2 . total = 40​

Answer 1

Answer:

Class interval Frequency Cumulative frequency

0−10 f

1

f

1

10−20 5 5+f

1

20−30 9 14+f

1

30−40 12 26+f

1

40−50 f

2

26+f

1

+f

2

50−60 3 29+f

1

+f

2

60−70 2 31+f

1

+f

2

N=40

⇒ Median=32.5, then 30−40 is class interval.

⇒ l=30,cf=14+f

1

,f=12 and h=40−30=10.

⇒ N=40,

2

N

=20

⇒ 31+f

1

+f

2

=40.

⇒ Then, f

1

+f

2

=9 ----- ( 1 )

⇒ Median=l+

f

2

N

−cf

×h

⇒ 32.5=30+

12

20−(14+f

1

)

×10

⇒ 2.5=

6

6−f

1

×5

⇒ 15=30−5f

1

⇒ 5f

1

=15

∴ f

1

=3

Substituting value in equation ( 1 ) we get,

⇒ 3+f

2

=9

∴ f

2

=6

∴ f

1

=3,f

2

=6