What is a set of 5 positive numbers that has a median 10 and mean 14?

One way to do this would be to assume that four the numbers are 10 (this guarantees that the median is 10.) Now all that is left is to find the fifth number that would make the mean to be 14. We need the average of the numbers to be 14, so we can write the equation: (10 + 10 +10 + 10 + x)/5 = 14where x is the number we need to find. The equation can be simplified:

(40 + x)/5 = 14

8 + x/5 = 14

x/5 = 6

x = 30.So one possible set of numbers is {10, 10, 10, 10, 30}.

(There are many other possible sets as well.)