The mean of these five numbers is 4, meaning the total of these five numbers is 20 since 4x5=20. Therefore all the numbers in these sets of numbers have to be smaller than 20. However, it has to have at least two 3’s, as the mode is 3. The biggest possible number between these data sets is 11, since there must be at least two 3’s, 20-6=14, but you must subtract 6 because 3+3=6. As well as this, you cannot use two 2’s because that will mean that there are 2 modes. We know that there are only 11 data sets because you have to consider the amount of 3’s that can be used and the total amount of these numbers added together.
All the sets you can make are: ( Put in order based on the size of the largest number )
[1, 2, 3, 3, 11]
[1, 3, 3, 3, 10]
[1, 3, 3, 4, 9]
[2, 3, 3, 3, 9]
[1, 3, 3, 5, 8]
[2, 3, 3, 4, 8]
[3, 3, 3, 3, 8]
[1, 3, 3, 6, 7]
[2, 3, 3, 5, 7]
[3, 3, 3, 4, 7]
[3, 3, 3, 5, 6]