How to add and subtract values from an average? Say I have 100 numbers that are averaged:
number of values = 100
total sum of values = 2000
mean = 2000 / 100 => 20

If I want to add a value and find out the new average:
total sum of values = 2000 + 100
mean = 2100 / 101 => 20.79

If I want to subtract a value and find out the new average:
total sum of values = 2100 - 100
mean = 2000 / 100 => 20

It seems to work, but is the above correct?
Is this the proper way to add/subtract values from a average without having to re-sum all the 100 numbers first?
 A: I know that's an old thread but I had the same problem.
I want to add a value to an existing average without calculate it back to the total sum.
to add an value to an exisitng average we only must know for how much values the average is calculated:
$$
average_{new} = average_{old} +  \frac{ value_{new} - average_{old}}{size_{new}}
$$
A: $s=\frac{a_1+...+a_n}{n}$. 
If you want the average of $a_1,...,a_n$ and $a_{n+1}$, then $s'=\frac{a_1+...+a_n+a_{n+1}}{n+1}=\frac{ns+a_{n+1}}{n+1} = \frac{(n+1)s+a_{n+1}}{n+1} - \frac{s}{n+1} = s + \frac{a_{n+1}-s}{n+1}$
If you want the average of $a_1,...,a_{n-1}$ then $s''=\frac{a_1+...+a_{n-1}}{n-1}=\frac{ns-a_n}{n-1}= \frac{(n-1)s-a_n}{n-1} + \frac{s}{n-1}=s+\frac{s-a_n}{n-1}$.
A: To put it programmatically, and since the question was about how to both add and subtract:
Add a value:
average = average + ((value - average) / nValues)

Subtract a value:
average = (average * nValues - value) / (nValues - 1)

A: Another formula can be
$$\text{NewAvg} = \frac{( \text{OldAvg} \cdot \text{OldSize} ) + \text{NewValue} } { \text{NewSize}}$$
