Notes for September 3, 1999

Discuss homework

Ask especially about making a caption for the histogram. Say that we realize that this is difficult, because a good caption should capture all that is going on, and there is a lot going on. Also, remind them that long captions are okay when short ones don't work.


A histogram showing 2000 random samples, each having500 students, recording the number of students in each sample who answered "yes" to the question of whether they believed they could be president.

Quickie questions (7 minutes)

Quantifying variability

Observations that came up during class
  • The two collections have different numbers of samples. ("Yes, I did that on purpose. It makes it harder to form judgements by eyeballing them.")
  • The two collections have the same range, so if we went strictly by range they would be equally variable.
  • But the top collection looks more spread out. If we go by how far apart the individual samples are, the Collection A is more variable.
  • But the bottom one has more samples, and more of them are farther away from 0.56. So, if we went by how many samples are farther from the center, Collection B would be more variable.
  • Beta said "But if you look at how evenly they are spaced, they are both spaced about as even."

I took Beta's observation as an opportunity to describe one conventional way to look at variability. It is to look at what fraction of the samples appear within various ranges.

If we look at what fraction of the statistics caclulated from each group lie within, say ±0.003 of 0.56, we see that in Collection A we capture 5/13 of the samples and in Collection B we capture 10/26 of the samples. So the two are very close in variability by this measure.