Answer: {5, 6, 7, 8, 10, 12, 13, 14, 15}
Other answers are possible.
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Step-by-step explanation:
Let's say 10 is the median, and we'll have four values above it and four below. This gives 4+1+4 = 9 total items. One such example could be {6,7,8,9,10,11,12,13,14}. This is the set of whole numbers from 6 to 14 inclusive.
Due to the symmetry of that list, the mean = median = 10
The only problem is the max is 14, when we want it to be 15. We can fix this by adding 1 to each of the upper four values {11,12,13,14} to get {12,13,14,15}.
To balance things out, subtract 1 from each of the lower four values. So we go from {6,7,8,9} to {5,6,7,8}. This balancing is to keep the mean the same at 10.
Therefore, the set {6,7,8,9,10,11,12,13,14} becomes {5,6,7,8,10,12,13,14,15} which is one possible answer.
There are infinitely many other possible answers. The data set does not have to be symmetric like this.