### 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.

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.

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.