# Central Limit Theorem Experiment

I have an idea for a Central Limit Theorem (CLT) experiment. I’d very much welcome comments from those in a position to help.

I’ve numbered 100 poker chips so that the frequencies are as given here:

My plan is to get students to pick out 10 from a box and record the mean.

If each student repeats this 10 times and we pool our answers.

**My Questions:**

1) Am I right in thinking that a bar chart of the means they get should look (approximately) like a Normal Distribution with:

2) How much does the fact that I’m using discrete data get in the way?

3) Are there any easy adjustments I could make to improve this?

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I think yes – after a fashion. The discrete data will mean that all of the means recorded will be multiples of 0.1, but I’d expect the shape to be normal-ish.Question 2 is whether you have enough trials – I’d suggest pooling students’ results (maybe in groups of 3 or 4), as the CLT only really takes hold when n>30 or so.The other issue may be that the distribution is truncated at 10 – eyeballing it, I don’t think it’ll be a huge problem (I’d estimate the mean to be about 7 and the SD to be about 3 – so the SD of the means would be about 1, and 10 would be three sigma, already pretty low). Hope that helps!

Thanks for that.I should have said that each student will do it 10 times and we’ll put all the results together. Approx 120 results.Your estimate of the mean prompts another nice little activity too!Dave