Solved – Making up datasets with matching or distinct summary statistics

4) Make up three data sets with 6 numbers each that have:
a) The same mean but different standard deviations.
b) The same mean but different medians.
c) The same median but different means.

Can anyone tell me the procedure of finding the data sets which match the above mentioned criteria.

For a), an example could be $$D_1 = (1,2,3,4,5,6)$$ $$D_2= (0,1,2,5,6,7)$$ $$D_3=(-1,0,1,3,6,12)$$ the mean is 3.5 for all three but the standard deviations differ. Can you figure out the rest?

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