Question

Create a data set of 10 numbers where the mean is less than two-thirds the median.

Answer 1

Our motive is to increase the median sufficiently and to decrease the mean sufficiently so that there is a sufficient gap. Obviously, our median will be the average of 5th and 6th number So we can have very large values for 6 numbers or we can have the same large values for 6 number. Let it be like 10

So, we have now 10,10,10,10,10,10

Now for decreasing the mean, we will choose very small values for the rest of the four numbers. Let it check with 1,1,1,1 . Then the mean is less than 2/3rd of the median. Mean is 6.4.

Thus one set of numbers can be 10,10,10,10,10,10,1,1,1,1