User blog comment:BunsenH/Uncertainties/@comment-25404524-20160923025356/@comment-24577221-20160924013433

Okay -- here's a sort-of demonstration.

I took the data from the first 180 lines in Abedshark's spreadsheet, and divided it into 18 groups of 10. In each group, I tallied the numbers of coins, diamonds, and steps/stars; that's 3 "measurements" in each group, so 54 "measurements". Each group has 30 items, averaging 10 each of coins, diamonds, and steps/stars. But as you know, individual experiments don't often match the statistical averages; in theory, the number of coins in a group could be anywhere from 0 to 30, ditto diamonds and steps. So plotting the number of times each number came up against the numbers, we get:



Which has kind of the shape I described.

It's not a perfect demonstration, because the shape of the curve is somewhat skewed -- 10 is the most common value, but possible values range from 0 to 30. And the values within each group aren't independent, since the three values within each group add up to 30. It would be more appropriate to just look at, say, the numbers of coins. But there just isn't enough data yet to give a smooth curve; even using all of the 54 numbers, that chart is pretty rough.