What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?
1 Answer
The average is 100.
Explanation:
The simplest method:
Take the average of the outermost two numbers. This will be the same as the average of all 19 numbers, because the numbers in between are evenly spaced out, in a symmetrical pattern.
The longer method would be to expand the expression, and solve manually, or using Gauss's method:
Factor a 10 out of the numerator:
To add the whole numbers from 1 to 19, use Gauss's method:
So, back to the expression: