Question

The median of the list

n, n+3, n+4, n+5, n+6, n+8, n+10, n+12, n+15

is 10. What is the mean?

Answer 1

11

Explanation:

The middle number in the 9-number list is
`$n+6$`, which is given as 10. Thus
`$n=4$`. Add the terms together to get
`$9n+63 = 9\cdot 4 + 63 = 99$`. Thus the mean is
`$99/9 = \boxed{11}$`.

Answer 2

The mean is given by


`\frac{n+(n+3)+(n+4)+(n+5)+(n+6)+(n+8)+(n+10)+(n+12)+(n+15)}9=\frac{9n+63}9=n+7`

The median is
`n+6=10`, which means
`n=4`, and so the mean is
`4+7=11`.