# Probability of $n$ numbers picked from set to have greater mean than set

If we have (N) varying non-negative numbers , with a mean equal to X, and a median less than X, if we pick (n) unique numbers from the set, what is the formula for the probability that the mean of those (n) will be greater than X?

(This is in a way trying to calculate for numbers that may weight the mean: for example numbers may be 3,4,5,6,7,8,9,10,11,12,21,30 with a mean of 10.5, and a median of 8.5, but say if (n) is 4, even if the picked numbers fall immediately above the median, their mean will fall below X. In this example (alone) you must have one of the last two numbers in your smaller set to have a higher mean: but even then, it depends on how low in the range the other 3 picks are)

• As you point out, the answer very much depends on what numbers are in our original set. – André Nicolas Jun 23 '16 at 22:26
• True, but we can calculate a mean and count a median regardless of what numbers are in the set, we can also calculate how many multiples away from the mean each number is, what probability each number has of being picked, and what weight that size and probability will have on the smaller sets mean... – mehmetic Jun 24 '16 at 1:31