ExplanationLet us assume there are 10 students (one for each quantile)

So let the scores be:

1, 1, 2, 2, 3, 3, 4, 4, 5, 5

In this case, adding up two lowest quintile students would be 1 + 1 = 2, which is less than 5, the score of a top quintile student.

So let the scores be:

10, 10, 11, 11, 12, 12, 13, 13, 14, 14

In this case, adding up two lowest quintile students would be 10 + 10 = 20, which is greater than 14, the score of a top quintile student.

Thus, you cannot determine which quantity is larger.
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Sandy

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