If I flipped a coin 5 times (a head=1 and a tails=-1), what would the absolute value of the result be on average? I.e., if I flipped five non-absolute values, then averaged them, then got the absolute value as the result, and I did that infinite times, what would be the average value of the result?
What mathematical method would I use to calculate this? I've only taken up to precalculus and I anticipate that calculating this would involve something I haven't learned yet but I don't know what it is.
Edit: I am asking this to understand how I can quantify how much lower sample size rather than an actual shift in the average for which there is a tendency can be expected to cause a deviation.

There are 32 different equally probable outcomes of 5 throws, of which two have absolute value of sum of throws equal to 5, 10 have 3, and 20 have 1, so total sum of all these cases is $5\times2 + 3\times10 + 1\times20 = 60$. To get average, we need to devide 60 by number of total cases which is 32. $\frac{60}{32} = \frac{15}{8}$. That is expectation of sums, average is sum divided by 5, so if you want to get expectation of averages, then you divide expectation of sums by 5 and get $\frac{3}{8}$.
