NDA 2017 Mathematics question

A sample of 5 observations has mean 32 and median 33. Later it is found that an observation was recorded incorrectly as 40 instead of 35. If we correct the data, then which one of the following is correct?

(A)The mean and median remain the same
(B)The median remains the same but the mean will decreaseCorrect
(C)The mean and median both will decrease
(D)The mean remains the same but median will decrease

Answer: (B)

Solution

Replacing 40 by 35 lowers the total by 5, so the mean falls from 32 to 31. Both 40 and 35 are greater than the median 33, so the corrected value

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Question ID VK-028688