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Problem says mean should be least possible.So we should try to keep the numbers as small as possible.

6 is the median,middle number.So there are 4 numbers greater than 6 and 4 numbers less than 6.

Mode is 25 only.So one of the numbers is 25.But it is the only mode,so there should be one more 25 to make it "the only mode".

Still we donot know the 4 numbers less than 6 and the 2 numbers greater than 6.We need to keep the numbers as small as possible.So, the 4 numbers that are less than 6 can be 1,2,3,4 . cant go smaller than that.Similarly missing two numbers that are greater than 6 are 7,8 (smallest possible).

So numbers are 1,2,3,4,6,7,8,25,25.
phew....lengthy explanation.

Problem says mean should be least possible.So we should try to keep the numbers as small as possible.

6 is the median,middle number.So there are 4 numbers greater than 6 and 4 numbers less than 6.

Mode is 25 only.So one of the numbers is 25.But it is the only mode,so there should be one more 25 to make it "the only mode".

Still we donot know the 4 numbers less than 6 and the 2 numbers greater than 6.We need to keep the numbers as small as possible.So, the 4 numbers that are less than 6 can be 1,2,3,4 . cant go smaller than that.Similarly missing two numbers that are greater than 6 are 7,8 (smallest possible).

So numbers are 1,2,3,4,6,7,8,25,25. phew....lengthy explanation.

lengthy but clear. Thanks for taking time to break it down because now i do understand it.

Problem says mean should be least possible.So we should try to keep the numbers as small as possible.

6 is the median,middle number.So there are 4 numbers greater than 6 and 4 numbers less than 6.

Mode is 25 only.So one of the numbers is 25.But it is the only mode,so there should be one more 25 to make it "the only mode".

Still we donot know the 4 numbers less than 6 and the 2 numbers greater than 6.We need to keep the numbers as small as possible.So, the 4 numbers that are less than 6 can be 1,2,3,4 . cant go smaller than that.Similarly missing two numbers that are greater than 6 are 7,8 (smallest possible).

So numbers are 1,2,3,4,6,7,8,25,25. phew....lengthy explanation.

Originally posted on MIT Sloan School of Management : We are busy putting the final touches on our application. We plan to have it go live by July 15...