 I’m thinking of four numbers. The mode of the numbers is 7; the median is 7.5; the mean is 9.

What are the numbers?

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First, you need definitions:

MODE: The most popular, or most frequently occurring item of data

MEDIAN: The middle number when the data set is ordered. If there are four numbers (as in this case) the median is exactly half way between the second and third values.

MEAN: This is calculated by working out the total of your numbers, and then dividing by how many numbers you have.

Here are the steps to solve the puzzle:

1) If 7 is the mode, then two of our numbers will be 7. We cannot have three 7’s, because this would affect the median. Our numbers are therefore 7, 7, x, x

2) If the median is 7.5, our third number is 8, because 7.5 is exactly half-way between 7 and 8. Our numbers are now 7, 7, 8, x

3) If the mean is 9, then the total of our numbers is 36, because 9 = 36/4. At the moment, our numbers total 7+7+8=22. This means that our last remaining number is 14, making our numbers 7, 7, 8, 14.

If you enjoyed solving that problem, then try this:

I am thinking of five numbers. The smallest number is 10. The range is 9. The mode is 11. The mean is 13. What are the five numbers?

NB RANGE: The difference between the highest and lowest values.