Expert: Chanda Walker - 2/25/2009

Question
There are 6 whole numbers in a set of numbers. The least number is 8, and the greatest number is 14.  The mean, the median, and the mode are 11.  What are the numbers?

Answer
s, t, u, v, w, x are our numbers.

s = 8
x = 14
The median is 11 so let's let v be 11.


so

t + u + v + (8 + 14 + 11) = 66   (66 = 11*6 since mean is 11 and there are 6 numbers)

t + u + v + 33 = 66
t + u + v = 33

There is more than one solution.
t = u = v = 11

Or

t = 10
v = 12
u = 11

Or

t = 9
v = 13
u = 11

Without more information, any of these solutions work.  I used 11 twice since it said the mode was 11 but technically, if there is an even number of samples and there is not more of one quantity than any of the others, the mode is equal to the mean.