The range of five numbers is 10, the mean is 13.6, the median is 14,
and there is no mode. Find a possible data set.

8 13 14 15 18.

Step-by-step explanation:

The median (the middle number) is 14 so we have

x x 14 x x       where x is a single number with each number being different (as there is no mode).

The mean is 13.6 so we have the total numbers

= 13.6 * 5 = 68.

The  4 numbers left must total 68-14 = 54 and the difference between the highest and lowest is 10.

I sense that the lowest and highest will add up to  about 1/2 of 54 so:

Try 8 and 18 for these last 2 numbers

The list would be 8 x 14 x 18.

The 2 numbers left will add up to 54 - 26 = 28 . One of these must be < 14 and the other > 14.  13 and 15 would fit.

So a possible data set  is:

8 13 14 15 18.

practice. practice. practice.