| Hand in
(review: p. 14, 1.8) p. 19 1.10 (time: trend&cycles)
p. 32 1.28 (C-sec. mean and med.)
|
Read, to discuss (be able
to answer in class)
p. 69 1.74 (hospital discharges)
p.45, 1.46 (net worth) &47 (athletes)
|
Optional
(review: p. 14, 1.7 describe lighning, Shakesp.) p. 22ff, 1.21 (time: flu-lag) |
What do we see?
What can we infer?
(Introduction)
Data source? Lurking
variables?
(pulse: stair climb)
Variability happens (Skewed
heights this term). Things settle down on average, BUT inferences
are never certain.
Statistics gives us a language
for talking about uncertainty.
HW questions?
Time plot. (pp. 17-19) Time
on horiz. axis, values on vertical. trend? (general
slope up or down). Cyclic?.
--Beware of extrapolation
--predicting a time trend into the future.
-- Research data: time, or order of
taking measurements, is often a lurking variable. Always do
a time plot.
Section
1.2: Summarizing distribution info with numbers
Measures of middle (central tendency)
--Colloquially
"average" can refer to any measure of middle, so watch out; be more
specific.
Mean (most common "average"):
Take sum (aggregate) of all observations and divide by how many (n)
Metaphors.
1) Center of gravity, balance point
of histogram.
2) Slice off bits from the big and add to
the little till everyone has the same.
(Or "aggregate"--total-- it all and portion it out evenly.)
Outlier
or long tail will pull mean in that direction (think seesaw balancing)
"Sensitive" to outliers, skewness.
Especially
useful: 1) For symmetric, tidy distributions
2) When metaphor 2 makes sense--looking for "fair share" of a total.
Median: half are bigger,
half are smaller
Point
on histogram with half the area to the left, half to the right.
Calculating:
Put observations in numerical order (stemplot!).
Middle one if n is odd, or average the 2 middle if n is
even.
Formula: Count in how far? (n+1)/2 places. (7
1/2 places? go halfway =average the 7th and 8th observations)
"Resistant
to skewness and outliers"--trimming off ends will make little difference
in median value.
More
"typical" than mean, if there is skewness or outliers.
(Badly bimodal distribution--"middle"
doesn't mean much.)
Symmetric distribution:
mean
= median
Author's website http://www.whfreeman.com/scc
Select a Category, choose "Statistical Applets",
Mean &Median.
Check out symmetric, skewed, distributions with outliers.
Measures of Spread (dispersion, variability)
next:
Range: largest
- smallest. Resistant? NO! Two observations carry
all the info; the rest could be anywhere.
Dot plots of 3 distributions, all with same
range:
.
.
.
.
.
.
.
.
__________
We need measures of spread that will better take into account all
the observations:
..........
__________
Quartiles, five-number summaries, boxplot, InterQuartile Range. (HANDOUT)
..
..
. .. .
__________
Variance, Standard deviation.
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