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.

In addition to the excellent answers by Sextus Empiricus and Dave, when you don't know how to approach a problem, a naive but very effective way to get an approximate answer is by just simulating the process you describe.
In R you could do this as follows:
set.seed(1234)
MC <- 1e5
x  <- numeric(MC)
for(i in 1:MC){
    x[i] <- abs(mean(sample(c(-1, 1), 5, replace = TRUE)))
}
mean(x)

Which results in 0.37564, fairly close to the actual answer. Even when you think you know how to answer a question, simulation can still be useful to 'check' your results.
