Discussion
Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?
Answer: C
The statement that must be true is At most half the candidates have a score that is larger than the median.
By definition, the median splits the ordered scores so that at least half are at or below it and at least half are at or above it. So no more than half can lie strictly above it, whatever the shape of the distribution.
The mean and median can be in either order: a distribution skewed to the right has its mean above the median, one skewed to the left has its mean below it. So neither 'median at least the mean' nor 'mean at least the median' must hold. And far more than half the candidates can score above the mean, if a few very low scores pull the mean down.
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