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Question

The median of the distribution given below is 14.4. Find the values of x and y, if the total frequency is 20.
Class interval:  0-6     6-12     12-18     18-24     24-30
Frequency:      4          x          5            y          1


Solution

Class Intervals Frequency Cumulative frequency(cf)
0-6 4 4
6-12 x 4+x
12-18 5 9+x
18-24 y 9+x+y
24-30 1 10+x+y
  f=10+x+y=20  

We have, Median=14.4
Clearly, it lies in the class interval 12-18.So, 12-18 is the median class.
∴ l=12, h=6, f=5 anf F=4+x and N2=10
So, 
 Median=l+N2Ff×h


=>14.4=12+10(4+x)5×6


=>2.4×56=10(4+x)


2=6x    ;   x=4

and  also,
10+x+y=10
⇒10+4+y=20
⇒y=6
answer= x= 4 and y= 6


Mathematics
RD Sharma
Standard X

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