7.1 An introduction to the normal curve

Once again I opted to introduce the shape of random distributions by randomly distribution foam plastic necklace beads on the floor.

This term I did not stand on a table or a chair, opting for a tighter cluster on the floor. I had the "bright idea" of trying to obtain distributions both by tile columns and tile rows. 

The narrower distribution was two to four rows less expansive. 

The Tripltek tablet was what made this possible. I could crawl around on the floor and enter data into a Google Sheet using the tablet, and have that data immediately available on the Smartboard.

I already had the column relative frequency and normal distributions  set up. The spreadsheet calculates an estimated mean and standard deviation for the bead distribution and feeds that into a normal distribution function. 

The (x-mean)^2*frequency is summed and then divided by the sample size, the square root of which is the estimated sample standard deviation.

A third table "rotates" the column data (which is in one row) into a column for graphing purposes. Only the one normal distribution is included. 

A hand waving argument is made that the bead distribution is roughly normally distributed.

The "hand-waving" argument on the Smartboard along with the mean and the inflection points. 

The curve was then moved over to Desmos to look at areas under the curve. I did not expect to get this far - I had thought the bead tally process would have taken longer. 

Showing the inflection points.

Harder to demonstrate is that any slice through the centroid will be roughly normally distributed.