Sums and averages

Given $n$ numbers $a_1, a_2, ..., a_n$, their sum is $a_1 + a_2 + ext{...} + a_n$. Their average (arithmetic mean) is $\text{Average} = \frac{a_1 + a_2 + \cdots + a_n}{n}$

Important properties

• The sum is simply the total when all numbers are added together.

• The average tells you what value each number would be if all were equal and their sum stayed the same.

• If you know the average and the number of numbers, you can find the sum: $\text{Sum} = \text{Average} \times n$.

• Adding or removing numbers changes both the sum and the average.