# Choose the mean

Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.

Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.

*This problem is adapted from the World Mathematics Championships*

The median and the mean are both smaller than 9, so the other numbers must be smaller than 9.

_ _ 9 9

The median will be halfway between 9 and the next largest number, so if the median is 8, then the next largest number must be 7.

_ 7 9 9

Then 9, 9, 7 and the fourth number must have a mean of 7, so, since there are 4 of them, they must have a total of 7$\times$4 = 28.

So the numbers are:

3 7 9 9