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?

**Solution:**

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.

If you’re feeling brave, post your solution below!