The median of 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

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is increased by 2

is decreased by 2

is two times of the original number

remains the same as that of the original set

answer is D.

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Detailed Solution

Given that, median of 9 distinct observations is 20.5.
Median divides the data into upper half and lower half observations.
Here, the number of observations n=9 which is odd.
Therefore, median is the

n + 1 2 th

observations.

9 + 1 2 = 102 ⇒ 5

Now, fifth term is 20.5 (Median).
The largest four observations are the 6th, 7th, 8th, and 9th observations.
Therefore, increasing the largest four observations by 2 doesn’t affect the median.
So, the median remains the same.
Therefore, option (4) is correct.

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