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

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++