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Picture these scores on a graph.,.It's a tall peak at 5 (63 people) and then tails off to only 3 each at 9 & 10.

The mode is the most common score (5).
The mean is the arithmetic average (5.79.)
The median is the point half way between the max & min scores (7)

When the results fall into a bell-shaped curve, the mean, median and mode are all the same.

The logic of the median in your explanation doesn't even make sense to me unless the number of votes for the highest and the lowest were the same.
Even the number of votes was of no importance, with the existence of bunch other scores, it still seems like a weird and pointless average because it doesn't encompass every value (score) in the question.

I don't know but to me, the median which you used "the mean" for, is the only true average that matters which the questions would typically ask for.

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