The median of the following data is 525. Find the values of x and y, if the total frequency is 100. Here, CI stands for class interval and Fr for frequency. CI 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 800-900 900-1000 Fr 2 5 x 12 17 20 y 9 7 4
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Correct option is
D
x=9 y=15
Computation of Median
Class intervalFrequency (f)Cumulative frequency (cf)0-10022100-20057200-300x7+x300-4001219+x400-5001736+x500-6002056+x600-700y56+x+y700-800965+x+y800-900772+x + y900-1000476+x + yTotal = 100We have,
N=∑fi=100
⇒76+x+y=100⇒x+y=24
It is given that the median is 525. Clearly, it lies in the class 500−600
∴l=500,h=100,f=20,F=36+x and N=100
Now,
Median=i+f2N−F×h
⇒525=500+2050−(36+x)×100
⇒525−500=(14−x)×5
⇒25=70−5x⇒5x=45⇒x=9
Putting x=9 inx+y=24, we get y=15.
Hence, x=9and y=15.
Step-by-step explanation:
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