### A visible normal distribution using soft foam plastic beads

I had introduced the normal curve on Wednesday via a class exercise involving the tossing of ten pennies multiple times. The three sections built up a normal curve. On Friday I began with a normal curve on the board.

The vertical lines at the bottom were aligned to the lines between the tiles in the floor. Although the tiles were one foot on an edge, I treated them as if they were 30 units on an edge, roughly 30 centimeters.

At 8:00 I was not thinking carefully and placed the stool as seen above, which put zero in the middle of a tile.

I then three bins worth of beads into the air while standing on the stool. Vertical throws as high as the ceiling. This proved to be a tad too many - the counts were really high between the inflection points. Counting was hard because I had to do counts at half-way between the lines.

At 9:00 I adjusted the stool.

A wider angle view of the distribution of the plastic beads on the floor.

This lined up the tile lines with the lines on the board above. I also tossed only two bins of beads, making the counts more manageable but increasing the risk of a non-normal distribution.

There is a two-dimensionality to the distribution, while my counts are one-dimensional slices. My sense is that the two-dimensional distribution means that the one-dimensional slices will not contain the correct percentage of beads, but the numbers worked out well enough to illustrate what is meant by "68% of the data will between plus and minus one standard deviation."

Counts were done manually. At 10:00 I started to sweep beads into piles of five, but then I realized I could not move the beads because one standard deviation would eventually land at 40 cm, and I would be forced to go back and recount the beads between plus and minus forty centimeters to show that the number was near 68%.

The distributions would be visually more normal than I could have hoped for. Note that the counts happen "between the lines" so that in the table I use the midpoint of each tile column as the class value. Thus 15 is the class for beads between 0 and 30 centimeters.

 Three bead bins Two bead bins Two bead bins x M8 f M9 f M10 f All sxn -195 0 0 0 0 -165 0 1 0 1 -135 3 2 2 7 -105 6 5 8 19 -75 11 10 11 32 -45 56 31 47 134 -15 101 79 75 255 15 99 70 63 232 45 27 31 45 103 75 7 5 10 22 105 6 4 4 14 135 2 1 5 8 165 0 0 1 1 195 1 1 225 0 0 318 239 272 829

Only the ten o'clock class had a significant visual departure from a nice normal curve. Maybe throwing three bins of beads is preferable given the more symmetrical curve seen at 8:00.

Standing on the stool did raise the concern of some students as to whether their doddering old professor would fall. I had to assure them that my balance was still good and that I do not normally fall. At least not 95.45% of the time.