Day 24: Heart of Mathematics

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Announcements:
- For today: you were to read section 7.5: Collecting Data Rather than Dust (this is the "lying" part!;)
- Section 7.6: Mindscapes #5, 6, 9, 23, 26 (type up #22) Due Monday, 10/27
Section 7.6: What the Average American Has
- Heights of our class
  - Constructing a histogram (using heights)
  - Interpreting measures of central tendency from the histogram
    - mean is the "center of mass" of the histogram
    - median is the middle value of the histogram
  - 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)
- Cicada population data
- Let's generate our own "normal data",
  - via coin tossing
  - StatCrunch using lots of coins
- What's not in a mean or median? Spread, or variation
  - How do we quantify variation?
    - "The mean difference from the mean" is one way....
    - Standard deviation is another. This is 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.
  - Interpreting measures of variation (from the histogram)
Section 7.5: Collecting Data rather than dust (the power and pitfalls of statistics)
- Assignment: pp. 581-: #1, 3, 4, 8, 12. These will be attached to your upcoming exam, coming up 11/3, and constitute 10% of the exam.
- We have an election coming up!
  - Why do all the polls differ?
  - What's this Bradley Effect? Or the Reverse Bradley Effect?
  - What is the Electoral College, and why can one candidate win more peoples' votes but lose the election?
- Sampling
  - Samples versus Populations
  - What is statistical bias?
  - Cicada population data
  - Avoiding bias. Mindscape #5, p. 581.
  - When is enough enough? Data, that is.
- Data we collect should be
  - accurate
  - unbiased
  - "sufficient in number to reflect the population's variability"
- How do we get honest answers to life's tough questions?
  - Are you rich?
  - Do you cheat on your spouse?
  - Do you have AIDS?
- Sampling with randomness -- sound like a good idea? Let's try....
- Let's answer an embarrassing question: are you male or female?
  - Let's calculate the true rates of maleness and femaleness in class...
  - Each person will flip a coin:
    - If it's heads, answer "Male"
    - 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.
  - An example: Mindscape #2, p. 581.
- How could we adapt this process to lose less of our data
  - with a die
  - with two tosses of a coin?
- Now: what embarrassing question should we now attempt to answer? Who's got something they really want to know?

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