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Question

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set _________.
(Data is arranged in ascending order)

A
is increased by 2
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B
is decreased by 2
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C
is two times the original median
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D
remains the same as that of the original set
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Solution

The correct option is D remains the same as that of the original set
Since n = 9 (odd observatioons), Median = (n + 12)th
then median will be
Median = (9 + 12)th=5thobservation
Now, last four observations are increased by 2.
The median is the 5th observation, which remains unchanged.

There will be no change in median.

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