Calculating average without knowing number of elements I would like to calculate the average of a a set of numbers without knowing the sum of the set. In other words, I want to calculate the average with knowing as little information as possible.
Note: I do not want to use $\frac{sum}{total}$ 
I am using looping (induction, I believe) to calculate the average. 
I would like to keep track of only one variable, say x, which is equal to the current accuracy.
Is it possible to calculate x without knowing sum?
In summary: seeking how can you calculate the new average knowing only the number of elements and the current average. 
 A: Notice that sum is the current average times the current number of elements...
Suppose that $a(n)$ is the average of the first $n$ elements of the set and $e$ is the $n+1^{\text{st}}$ element.  Then 
$$  a(n+1) = \frac{n a(n) + e}{n+1}  \text{.}  $$
Of course, all this does is reconstruct sum, update it with the new element and then divide to get the new running average.
A: You need to keep track of two numbers.  If you don't you don't know how much a new number changes the average.  Say the average of the first bunch is $100$ and you get a new one of $1$.  If the first bunch is just one, the new average is $50.5$.  If the first batch is $100$ the new average is about $99$.  
You can do it in a loop if you keep track of the current average $a$ and the number of items seen so far $n$.  This hides the fact that the total so far is $an$.  If you get a new value $d$ you can update the average to be $\frac {an+d}{n+1}$ and the count to be $n+1$.  In a sense this is doing the same thing, but you don't have to keep the whole list available.
A: Let us start with an example. 
Find the average of $$\{ 3,5,6,2\}$$
$$3+5=8,8/2 = 4$$
$$2(4)+6 =14, 14/3 = 14/3$$
$$3(14/3)+2=16, 16/4=4$$ 
Which is the final average. 
