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  4. M, M and M

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

Comments

Submitted by Mollie on Mon, 03/14/2016 - 14:26

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

Submitted by ajk44 on Tue, 03/22/2016 - 08:35

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

Submitted by Charlie on Mon, 03/14/2016 - 14:28

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.

Submitted by Elliott on Mon, 03/14/2016 - 14:30

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

Submitted by Jessie on Mon, 03/14/2016 - 14:31

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!!!

Submitted by Lilli Fraser on Mon, 03/14/2016 - 14:32

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.

Submitted by Shannon on Mon, 03/14/2016 - 14:34

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

Submitted by Lucy on Mon, 03/21/2016 - 14:14

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

Submitted by cfg21 on Tue, 03/29/2016 - 14:02

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