HW assignment Day3 (From Moore unless otherwise noted.)
Reading: rest of 1.1, 1.2: to p.
32 for this hw.
Ahead: For next assignment day 4: 5-number
summary and boxplots, to p. 37,
+ annotated 5-number summary page handout (Will
behanded out
next time),
+ ( standard deviation & summary), p. 37- 42.
Do the means and medians required here by hand (with a calculator).
Make the timeplot(s) by hand.
| 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) |
Stemplot: review, split leaf 5 ways.
(HW questions?)
Dotplot for shoe size.
Choosing a display (by hand): Note bottom of p. 38, fig.
1.12, use of a dot plot to display a data set of size n = 7.
A dot plot is
most useful for n = 3 to about 15-20, or when the data only fall on a few
values (just stack the dots up).
A stemplot is
good for continuous data, smeared around; you can do 100 values in 3-5
minutes.
What do we see?
What can we infer?
(Introduction)
Data source? Lurking
variables?
(pulse: stair climb)
Variability happens.
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.
| Sievers home | Math151-Fall04/Dayf3.htm | 11am | 9/1/04 |