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.

Since this appears to be a self-study question, I will give some guidance rather than solve it all.
You can be very formal about how to define average value (what statisticians and mathematicians would call an expected value), to which the linked content about the law of the unconscious statisticians refers. However, taking advanced proofs as given (they are, after all, true), the average you seek is the sum of the values resulting from your procedure (add up the values, then take the absolute value), with each value weighted by the probability of it occurring.
Define $v_i$ as the value arising from applying your procedure to flipping $i$ heads, so $v_5 = 5$, $v_0=5$, $v_2 = 1$, etc. Next, define $p_i$ as the probability of flipping $i$ heads, so $p_5 = p_0 = 0.5^5 = 0.03125$, etc.
Then the sum of the values weighted by the probability of obtaining that value, is:
$$
\overset{5}{\underset{i=0}{\sum}} p_iv_i = p_0v_0 + p_1v_1 + p_2v_2+p_3v_3 + p_4v_4 + p_5v_5
$$
Now just calculate those $p_i$ and $v_i$ values, and I've already given you some (but make sure you know how to calculate them). I think you will find $v_i$ trivial. For $p_i$, you will find life easier if you use the PMF of the binomial distribution, which is contained in the linked Wikipedia article in the comments (and again here).
