There are 7 whole numbers in a set of numbers. The least number is 10, and the greatest number is 20. The median is 16, and the mode is 12. The mean is 15. What are the numbers?

10, 12, 12, 16, 17, 18, 20

Step-by-step explanation:

The question has already given you most of the numbers - you can need to consider the different types of averages.

We know there is a 10, 12 (at least two 12's as it's the mode), a 16 and a 20. That's 5 numbers already.

As we know that 16 is the median, it HAS to be the 'middle' number - i. e. the 4th in the series (1st, 2, 3, 4, 5, 6 7th)

That means we can now be sure that there are 2 12's, as follows:

10, 12, 12, 16,?,?, 20

We know we need the mean to equal 15 so ...

Y/7 = 15, where Y is the sum of all 7 numbers

If we reverse this we can work out what the total of set needs to be

15*7 = 105

Therefore Y is 105

Adding the numbers we have so far together: 10 + 12 + 12 + 16 + 20 = 70

105 - 70 = 35

Therefore the last two numbers have to equal 35. As we know that 12 is the mode, one of the answers cannot be 16 as 16 would then also be the mode.

That means, as the numbers are all whole numbers, that the last in the set are 17 and 18.

To check this I then calculate the mean again:

10 + 12 + 12 + 16 + 17 + 18 + 20 = 105

105 / 7 = 15