Question

find the set of five items of data that has a range of 9, a mean of 11, a meadian of 12, and a mode of 15.

Answer 1

Here's what I've done:

Represent the set of 5 items by {a,b,c,d,e}.  Assume that these items have already been arranged in ascending order.  

The middle item, c, has the value 12.

Since "mode" means "most frequently appearing item," let's assume that d and e are both 15.

If the range is 9, we could then write 15-9 = 6, meaning that a = 6.

Then we have {6,b,12,15,15}

To find b, sum up {6,b,12,15,15}, equate the result to 11, and solve for b.