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Question

Find the median for the following data.

Observation367910Frequency8101598


A
3
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B
6
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C
7
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D
9
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Solution

The correct option is C 7

Sum of frequency is 50 or fi = 50 and calculate less than cumulative frequencies in the table.

observation (xi) frequency (fi) cumulative frequency (cfi)
3 8 8
6 10 18
7 15 33 (Median Class)
9 9 42
10 8 50
fi=50


Since, even number of observation so the median will be the average of
(n2)th = (502)th observation and (n2+1)th = (502+1)th observation i.e., average of 25th and 26th observations repectively.

The first 8 observations occurs 3 times, next 10 occurs times and next 15 occurs 7 times.

So, the 25th and 26th observation will be 7 and 7 respectively.

Average of 7 and 7 = 7 + 72 = 7
Thus, median of the given data is 7.


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