How to calculate moving average without keeping the count and data-total?

Question

You can simply do:

double approxRollingAverage (double avg, double new_sample) {

    avg -= avg / N;
    avg += new_sample / N;

    return avg;
}

Where N is the number of samples where you want to average over. Note that this approximation is equivalent to an exponential moving average. See: Calculate rolling / moving average in C++

New average = old average * (n-1)/n + new value /n

This is assuming the count only changed by one value. In case it is changed by M values then:

new average = old average * (n-len(M))/n + (sum of values in M)/n).

This is the mathematical formula (I believe the most efficient one), believe you can do further code by yourselves

From a blog on running sample variance calculations, where the mean is also calculated using Welford's method:

Too bad we can't upload SVG images.

Here's yet another answer offering commentary on how Muis, Abdullah Al-Ageel and Flip's answer are all mathematically the same thing except written differently.

Sure, we have José Manuel Ramos's analysis explaining how rounding errors affect each slightly differently, but that's implementation dependent and would change based on how each answer were applied to code.

There is however a rather big difference

It's in Muis's N, Flip's k, and Abdullah Al-Ageel's n. Abdullah Al-Ageel doesn't quite explain what n should be, but N and k differ in that N is "the number of samples where you want to average over" while k is the count of values sampled. (Although I have doubts to whether calling N the number of samples is accurate.)

And here we come to the answer below. It's essentially the same old exponential weighted moving average as the others, so if you were looking for an alternative, stop right here.

Exponential weighted moving average

Initially:

average = 0
counter = 0

For each value:

counter += 1
average = average + (value - average) / min(counter, FACTOR)

The difference is the min(counter, FACTOR) part. This is the same as saying min(Flip's k, Muis's N).

FACTOR is a constant that affects how quickly the average "catches up" to the latest trend. Smaller the number the faster. (At 1 it's no longer an average and just becomes the latest value.)

This answer requires the running counter counter. If problematic, the min(counter, FACTOR) can be replaced with just FACTOR, turning it into Muis's answer. The problem with doing this is the moving average is affected by whatever average is initiallized to. If it was initialized to 0, that zero can take a long time to work its way out of the average.

How it ends up looking