- Homework, Section 4.3 returned: Graded #2, 15
- Homework, Section 4.5 is due today.
- Homework for Section 7.6 due next time.
- Just for fun: A honeycomb (Mother Nature, mathematician)
- Some statistics:
- The average American has one testicle and one ovary.
- The average income for a Lakeside School graduate was $2.5 million (in 1997)
- What's in a mean? (it's a "center of mass"; the fulcrum
of a teeter-totter)
- The median American has no testicles and two
ovaries (there are more women than men in the
population).
- What's in a median? (it's easy to calculate, given the
distribution (the middle value in the sorted list of
data); it's generally typical; if there are even
numbers in the distribution, it's the mean of the
"middle pair")
- What's in a measure of center? (they're not necessarily
typical!)
- Visual display of data:
- What's not in a mean or median? Spread, or variation
- Results of our Activity: Heights (and
heads) of our class:
- Access StatCrunch
- As a group (human histogram)
- Men (to the right of the histogram)
- Women (to the left of the histogram)
Now: how do I respond to my son? How many heads tall is a person, anyway?
- Heights of people tend to be normally distributed (that is, show a bell-shaped curve):
- Normal distributions arise quite naturally
- hexstat
- Wasp masses
- How do we quantify variation about the mean?
- We are all deviants: we deviate from the mean.
- "The mean difference from the mean" is one way... but it ends up being useless: the mean difference from the mean is zero!
- "The mean distance from the mean" is one way... (it won't be zero, generally, because all the distances are positive).
- Standard deviation is another. This is a "typical deviation" from the mean, or a "standard deviation"...
- Interpreting measures of variation (from the histogram)
- Assignment from section 7.5: pp. 581-: #1, 3, 4, 8, 12.
These will be attached to your upcoming exam, coming up 4/8, and constitute 10% of the exam. There will likely be an additional problem on the exam like these, to show me if you really understand the procedure. - We recently had an important election.
- Did you notice that the polls were all over the place? That some groups went to a "Poll of Polls"?
- Why do polls tend to 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 -- are we biased?
- Avoiding bias (e.g. the Literary Digest and the Landon/FDR election of 1936). Mindscape #5, p. 581.
- When is enough enough? Data, that is. (Too little is bad -- e.g. Bad, Bad, Biltong)
- Gold standard: random sampling
- Data we collect in a sample should be
- accurate
- unbiased (reflect the population truly - random sampling helps)
- "sufficient in number to reflect the population's variability"
- But: How do we get honest answers to life's tough questions?
- Are you rich?
- Do you cheat on your significant other?
- Do you have AIDS?
- Sampling with randomness -- sound like a good idea? Let's
try....
- Activity: Let's answer an embarrassing question:
are you male?
- We'll attempt to 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 we'll have half the people say "Male" because they tossed a heads. The excess (above half) are truthful "male" answers.
- We guessed:
- M=7+8 (7 "true males", 8 "false males"))
- F=4 (4 "true females")
- True rate: 7/19
- Estimated rate: (15-9.5)/9.5=5.5/9.5=11/19
- Where did the 9.5 come from?
- More examples:
- Mindscape #2, p. 581.
- How likely are you to use your cell phone while driving?
- Now: what embarrassing question should we now attempt to answer? Who's got something they really want to know?
- How could we adapt this process to lose less of our data
(generalize, when you get a good idea!)
- with a die
- with two tosses of a coin?
