bellcurve wrote:From my understanding, mean = median if,
1. the set consists of evenly spaced numbers
2. if all the members of the set are equal
3. set has just one number

Is there any thing else? In DS type of "is mean = median" questions, what do you have to know to be sure that mean = median?

Yes, there is a lot more.

For every set of evenly spaced numbers (or an Arithmetic Progression), Mean = Median.

BUT

If Mean = Median for a set of numbers, then the set of numbers need not be an AP.

Let me show some sets of numbers which are not in an AP but for which mean = median:

(i) 2, 3, 5, 7, 8
(ii) 3, 4, 4, 4, 5
(ii) 1, 4, 5, 6, 7, 8, 11

Your turn now! Can you show me a few such sets of numbers?

Hint: Take any AP. Tweak a few terms in it so that neither the Mean nor the Median change and it no longer remains an AP.