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The median is larger than the average for which one of the following sets ... ...

The median is larger than the average for which one of the following sets of integers?
(A)    {8, 9, 10, 11, 12}
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Math - Problem Set AA: Probability & Statistics

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The median is larger than the average for which one of the following sets ... ... 
Posted: 05/14/2013 15:14
I do not understand this at all. The answer made no sense.
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Posted: 05/14/2013 21:35
Hi Drew. You can find the median pretty easily, right? That's just the number in the middle. Then for each number group, we need to find the mean. We don't actually need to do the complete arithmetic. "By symmetry" means we can conclude, eg, that the mean of 1,2,3 is 2, and the mean of 2,4,6 is 4. And the mean of 2,4,7 is larger than 4 (because the mean of 2 and 7 is 4+).

That way we can quickly find the number group whose mean is larger than the median. I hope this helps.
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