Median: place the numbers you are given in value order and find the middle number. When the number of numbers is even, the median is the average of the two middle numbers.
In this case we have 6 numbers, so the median (5) will be the average between the 3rd and 4th number when all the positive integers are put in increasing order. (C+D)=10
The next thing we use is the mode (8), which is the most popular value. In a list of 6 numbers we have either two or three 8s.
Now using a bit of common sense, we can say that C and D cannot both be 5, as that would limit us to have only two 8s as E and F, which would mean 8 could not be the mode. Therefore, let’s try C and D as 4 and 6.
Now we have A,B,4,6,8,8
We know that the mean is 5, so we can set an equation.
(A+B+4+6+8+8)/6 = 5 * times both sides by 6
A+B+4+6+8+8 = 30
A+B+26 = 30
A+B = 30–26
A+B = 4
A and B could both be 2, but that would remove the ‘mode status’ from 8. Therefore, A and B have to be 1 and 3 in that order.
The six numbers are: 1,3,4,6,8,8