The average (arithmetic mean) of a set of observations is their sum divided by their number.
1Basics
Average = sum of observations ÷ number of observations
Sum = average × number
2Standard results
Average of the first n natural numbers = (n + 1)/2
Average of the first n odd numbers = n; of the first n even numbers = n + 1
Average of consecutive numbers = (first + last)/2
3Adding or replacing
New number added = (new count × new average) − (old count × old average)
If replacing one item raises the average of n items by d, the new item = old item + n × d