Since eleven is odd, there must be a centra element, which in this case is the sixth. So, we can write 11 consecutive integers as
[tex] x-5, x-4, x-3, x-2, x-1, x, x+1, x+2, x+3, x+4, x+5 [/tex]
Since the arithmetic mean is the sum of the values, divided by how many they are, we have
[tex] M = \dfrac{x-5, x-4, x-3, x-2, x-1, x, x+1, x+2, x+3, x+4, x+5}{11} = \dfrac{11x}{11} = x [/tex]
So, the mean of 11 consecutive integers is the 6th integer.
