Crappy D20

A set of 250 throws with average of 9.56 in a fair d20 has a probability of about 0.5% to occur, so in 17 sets there is about a 8% chance to happen if you dice were fair according to binomial distribution. This means there is a 92% chance that your die is unfair. usually a confidence of >95% is needed for science but for home i think is enough to declare a dice unfair.

This calculation only says if the die is unfair, not how much unfair.

250 rolls is really low for a d20 test, not enough to spread out the randomness over all surfaces. 1000 is also on the low side, but has more chance to indicate a bias.

Very interesting statistical data set you have there, I'd be interested in replicating the outliers (particularly that 27 1's die) and if it isn't poorly shapen, don't reveal the follow-up stats and force the "cursed die" onto special rolls/annoying people in the party. If it is poorly shaped get rid of it imo,

Naughty d20s go in the microwave.

Oof that’s horrendous. Like the average is still around the same but the consequences are so so much worse

This is some hot data

Now I think you should test if averages hold consistent between same sided die from different manufacturers. I think another poster is right that the shape matters, so if the die from the same caster are molded roughly the same, then they’ll present with similar averages.