Question

31. The median of the following data is 16. Find the missing frequencies a and b, if
the total of the frequencies is 70.
Class
0-5 5-10 10-15 15-20 20-25 25-30
30-35
35-40
Frequency 12
4
a
12
15
b
6
6​

Answer 1

Answer:

Class Interval Frequency cf

0−5 12 12

5−10 a 12+a

10−15 12 24+a

15−20 15 39+a

20−25 b 39+a+b

25−30 6 45+a+b

30−35 6 51+a+b

35−40 4 55+a+b=70

Here:

N=70

N/2=35

Median =16, Median class =15−20

So, I=15, h=5, f=15 and

xf=xf of preceding class i.e.24+a

We know,

Median =1+{h×(n/2-cf)/f}

Substitute all the value in the above formula, we get

16=15+{5×(35−24−a)/15}

⇒16=15+(11−a)/3

or a=8

Now, 70=55+a+b

70=55+8+b

⇒b=7

so, missing frequincies are 8 and 7.