M, M and M

The set of five numbers $2, 3, 3, 5, 7$ has the following properties:

Their mean is $4$. Their median is $3$. Their mode is $3$.

Can you find other sets of five positive whole numbers which share the same properties?

How many different sets are there?

How can you be sure you've found all possible sets?

 Share your thoughts and discoveries


As long as the five numbers are positive and add up to twenty this should work. There must be at least 2 threes within the group of five numbers. Also, the numbers that are not threes should add up to fourteen.

ajk44's picture

That's very interesting Mollie. Can anyone explain why Mollie's rules are needed to solve this?

In this problem, the five positive numbers have to add up to twenty. There has to be at least 2 threes within your set of five positive numbers. Also the numbers that aren't the number 3 should add up to 14.
Thank you for reading.

Remember to always have two 3's when making your sets and make sure it adds up to 20!

To solve this problem the key rule is to have at least two three's to make sure you get the mode and median correct. To get the mean all the five numbers must add up to twenty. The last three numbers need to add up to fourteen. As long as follow those rules you will have no problem with the problem!!!

1. You must have at least two threes.
2. The three should be in the middle of the numbers when all numbers are ordered .
3. Five numbers.
4. Add up to 20.

Sometimes, people think before they start a wild maths problem ' this is going to be easy ' but when you finish your head is all jumbled up, even if you got the right answer. That's because wild maths is an inspiring, educative and life-changing website that encourages young children to really open up to all the possibilities in the world. M, M and M is a good way to start on averages.
Here are a few tips on solving the problem:
Your combinations must have at least 2 3's
It has to add up to 20
If the combination adds up to 20 you have to divide it by 4 to get an answer of 5

You have to have more than 1 three .To get 3 as the median you have to have two numbers lower than three. Your numbers have to add up to twenty or then the mean will not be 4.
you can have [these are not all the answers]:
1, 2, 3, 3, 11
2, 3, 3, 5, 7
9, 2, 3, 3, 3
3, 3, 3, 3, 8
1, 3, 3, 3, 10

Great - can you now find the rest of the possible sets of numbers?