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Question

# Compute the median for each of the following data:(i)MarksNo. of students (ii)MarksNo. of studentsLess than 10 0More than 150 0Less than 30 10More than 140 12Less than 50 25More than 130 27Less than 70 43More than 120 60Less than 90 65More than 110 105Less than 110 87More than 100 124Less than 130 96More than 90 141Less than 150 100More than 80 150

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Solution

## (i) Class intervalFrequency Cumulative frequency 0−100 0 10−3010 10 30−5015 25 50−7018 43 70−9022 65 90−11022 87 110−1309 96 130−1504 100 N=100 We have, N=100,N2=50The cumulative frequency just greater than N2 is 65 then median class is 70−90 such that,l=70,h=90−70=20,f=22,cf=43Median=l+N2−cff×h⇒ Median=70+50−4322×20⇒ Median=70+7×2022⇒ Median=70+6.36∴ Median=76.36(ii) Class intervalFrequency Cumulative Frequency 80−909 9 90−10017 26 100−11019 45 110−12045 90 120−13033 123 130−14015 138 140−15012 150 150−1600 150 N=150 We have, N=150, then, N2=1502=75The cumulative frequency just more than N2 is 90 then the median class is 110−120 such that l=70,h=120−110=10,f=45,cf=45Median=l+N2−cff×h⇒ Median=110+75−4545×10⇒ Median=110+30×1045⇒ Median=110+6.67∴ Median=116.67

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