Day 25: Heart of Mathematics

Today:

• Final project paper were due next Monday, 4/21; let's extend that to Wednesday, 4/23.
  • Visit the writing center!
  • Look for, find, and illustrate the mathematics.
  • The Schedule of presentations.

    Important:

    • You need to be there for your classmates.
    • If you are not in class for the other presentations, you will lose points on your own.

• Section 6.3 mindscapes due today

• Last time: Section 7.5: Collecting Data rather than dust (the power and pitfalls of statistics)
  • Assignment: Mindscapes pp. 581-: #1, 3, 4, 8; Type up 12. due Monday, 4/21

  • Sampling with randomness
    • Let's calculate the true rates of maleness and femaleness in class...
    • Each person will flip a coin:
      • If it's heads, answer "Male" (this should be the "embarrassing answer", to provide cover)
      • If it's tails, answer truthfully.
    • How do we now estimate the true rate?
      • Guess that half the "Male" answers are from heads; the other half are truthful answers.

  • How could we adapt this process to lose less of our data?

  • How would we choose an appropriate level of "data-loss", and "answer-protection"?

  • Now: what embarrassing question should we now attempt to answer? Who's got something they really want to know?

• Section 7.6: What the Average American Has (or had, in 1993)
  • Mindscapes #5, 6, 9, 23, 26 (type up #22) Due Wednesday, 4/23

  • Some statistics:
    • The average American has one testical and one ovary.
    • The average income for a Lakeside School graduate was $2.5 million (in 1997)

  • What's in a mean?

  • Let's try a different measure of "central tendency":
    The median American has no testicals and two ovaries.

  • What's in a measure of center?

  • Visual display of data:
    • What's not in a mean or median? Spread, or variation
    • Heights of our class
    • Heights of people tend to be normally distributed (if distinguished by sex); otherwise, if the sexes are combined, you might expect a bi-modal distribution
    • Normal distributions arise quite naturally (hexstat)
    • Cars

  • How do we quantify variation?
    • "The mean difference from the mean" is one way....
    • Standard deviation is another. This of this as a "typical deviation" from the mean, or a "standard deviation"...
    In any event, these measures help us to appreciate about by how much an individual measurement typically varies from the mean.

  • Some other innovative, ingenious, imaginative visual displays of data