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The median of a set of 9 distinct observations is 20.5. If each of the four largest observations in the set is increased by 2, what happens to the median of the new set?

1. The median increases by 2.
2. The median decreases by 2.
3. The median becomes twice the original median.
4. The median remains the same as that of the original set.

Correct answer: The median remains the same as that of the original set.

Solution

With 9 distinct observations in ascending order, the median is the 5th observation. The 'four largest' are the 6th, 7th, 8th, and 9th observations. Increasing these four by 2 does not affect the 5th observation, so the median remains 20.5.

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