You are completely right. Thanks for this observation.
10 samples/second = 864.000 /day = 6 million per week.
The number of samples is approaching the accuracy of the (IEEE754) float (7 digits) when one reaches 1 million samples (1 day in your case) . This means if the average sample has 3 digits, one will loose 2 digits every time.
The "trick" of remove one double and add one double is an efficient way to calculate the sum of the array of samples. And yes when using this trick the error will add up in sum. In theory after 100 samples the last two digits are suspected to be incorrect. Need to investigate the effect.
Solution is to (sort and) add all elements of the array every time, giving a constant error. Consequence is a slower execution. The sorting will improve the sum when the dynamic range of the numbers is large.
A practical solution for the library might be to do a proper sum e.g. every 100 or 1000 times a value is added (new parameter?). The lower this number the more accurate the sum. The price is a performance penalty once every 100 / 1000 times. There are several variations possible.
A good value for the number will also depend on the size of the numbers added. Ideally one would like to have a sort of error counter that makes an estimate of the max error and when a threshold is reached do a recalculation of sum.
The easiest solution is to redo the function Average() and rename the current one to fastAverage();
in short food for thought.
thanks