Question

Find two of the three possible numbers that can be placed in the set below so that the median of all 5 numbers would equal their mean.
{3, 6, 9, 10}

Answer 1

One way is to check the mean of the four numbers. See if inserting the number in the middle will work.
(3+6+9+10)/4=7.

Since 7 sits smack in the middle of the list, we can add 7 to the list so that the median equals the mean.

Now try the other two positions:

Any number inserted below the 6 will force 6 to be the median and the mean, and so the sum must add up to 30, thus the number to be added must be 2.

Numbers inserted after 9 will force 9 to be the median and the mean, and the sum must be 9*5=45. Thus the number to be added is 45-28=17.

The three possible numbers are therefore 2, 7 and 17.