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Question

Class Interval0-100100-200200-300300-400400-500500-600600-700700-800800-900800-900
Frequency25x121720 y974

The median of the following data is 525.

Find the value of x and y, if the total frequency is 100.


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Solution

Find the value of xand y:

Given,

Class Interval0-100100-200200-300300-400400-500500-600600-700700-800800-900900-1000
Frequency25x121720 y974

The value of the Median is 525

The Median Class is500600

Class IntervalFrequency(f)Cumulative Frequency (cf)
0-10022
100-20052+5
200-300x2+5+x
300-400122+5+x+12
400-500172+5+x+12+17
500-600202+5+x+12+17+20
600-700y2+5+x+12+17+20+y
700-80092+5+x+12+17+20+y+9
800-90072+5+x+12+17+20+y+9+7
900-100042+5+x+12+17+20+y+9+7+4

76+x+y=100x+y=24(i)

Median=l+N2cff×h

Since,l=500,h=100,f=20,cf=36+x andN=100

Consequently, when using the Median formula with the value,

we obtain:

Median=l+N2cff×h525=500+100236+x20×100525=500+5036-x20×100525-500=14-x20×10025=14-x×55=14-xx=14-5x=9

Put x=9 in (i),

9+y=24y=24-9y=15

Hence, the value of x=9 and y=15.


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