A mean of 25 a mode of 11 and a median of 14 and a range of 9 what are the 5 numbers in the data set?

Let write the data in an increasing order: p q r s t.

Since the median is 14, then r = 14, and we have: p q 14 s t.

Since the mode is 11, then p = q = 11.

Since the range is 9, then t - p = 9, t - 11 = 9, and t = 20.

So, we have: 11 11 14 s 20.

Since the mean is 25, we have:

(11 + 11 + 14 + s + 20)/5 = 25
(56 + s)/5 = 25 multiply by 5 to both sides
56 + s = 125 subtract 56 to both sides
s = 69

So the data set is: 11 11 14 69 20