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mean = 9

median = 6

mode = 6

So let the middle 3 numbers be 6. Now if we pick any two other numbers, the mode is 6. Also, since we have 3 6's the median will be 6 if the other two numbers are greater than 6.

All that is left is to pick two number such that when they are added to 6x3=18 and then divided by 5 we have a mean of 9. There are many choices, but 18, and 9 work.

So one possibility is

6,6,6,9,18

We could still have a mean of 9 if we use a number bigger than 6 and smaller than 6.

For example

5,6,6,6,22

The mean is not changed because 5 and 22 are still 27 and 6 is still the median and the mode.

There are infinitely many more answers.

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Q: What are five numbers with a mean of 9 and median of 6 and mode of 6?
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