I collect numbers from generators that yield different ranges of whole numbers with an unknown distribution. I want to estimate the mean of the numbers outputted by this generator. I'm convinced the distributions are symmetric (more specifically, uniform) though, so I can just average the min and max after I have a decent sample size.
What would be the best way to test that the distribution of numbers is symmetric or uniform?
Things I've tried:
-Checked that the mean, median, and midpoint converge to the same values, but I can't quantify how close the values would have to be.
-Histogram, but my sample sizes (n<100 because I must manually collect) are too low for me to tell
-Chi-square test with the frequencies of each number in the range and testing them against the expected value for a uniform distribution, but I've read there are problems with this in other posts
-Pearson's skewness coefficient and comparing that with the standard error of skewness, but I think there are limits to this kind of approach -Comparing kurtosis of data with that of a uniform distribution
I've also read about the Kolmogorov-Smirnov tests and Shapiro-Wilk tests but these seem too complicated for such a simple seeming task..