Can You Guess the Correct Number of Gumballs in this Machine?

There is a statistical theorem called the Central Limit Theorem that addresses this problem. If you want to get technical, you can research this theorem. I looked to Microsoft's co-pilot to explain it in simple terms. I wanted to make it understandable to school children with short attention spans.

If you want the most accurate average, it is best to have a large number of random educated guesses. The more guesses you have, the more likely you are to arrive at the correct answer.

Also, having a diverse group with a range of perspectives can lead to a better average that hits or gets closest to the correct number.

Here is my editorial opinion: I think the "wisdom of crowds" can be used in many ways. We all want to be right or think we have the best answer, and the best way of arriving at it. However, I think it would be far more interesting to see many different methods of trying to guess the correct answer. This way you can learn something about how different people think about different problems, and the many methods you might try. Keep in mind the gumballs have to stay in the machine. You cannot remove any during the contest, or else the number will change.