7.1 7.3 Random distribution of beads

Given the confusing bimodal soap distribution of last spring, I omitted that demonstration this term and went directly into the bead distribution.

Spreadsheet

This term I again only looked at the distribution horizontally. Simplify. I tried to make more clear than in past terms that the middle of the scattering of beads was the mean, and that somewhere out around one and half tiles up and down was one standard deviation away from the mean. I did this prior to counting the beads per tile.

The mean and standard deviation were generated by the spreadsheet.

The distribution was nicely normal with 253 beads thrown, 38 more beads than the spring 215 beads. I threw all rounds, hearts, stars, letters, and animals.

Smoothed out (the blue line) the distribution is only very slightly leptokurtic with a kurtosis of 0.074. Desmos was used to show that the red curve can be produced by just two values: the mean and the standard deviation. 

Desmos


I then previewed 7.3 in Desmos showing that the area holds the same as the mean and standard deviation change in the above Desmos diagram. 

Based on notes from fall 2023, changing examples between 7.1 and 7.3 is confusing for the students. The same distribution will be used to cover 7.3.


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