MATH 251, Probability and Statistics I, Fall 2007, Mon. Aug. 27, Day 2
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Unless otherwise noted, all assignments are in Moore & McCabe,
Intro
to the Practice of Statistics, 5th ed. ("IPS")
Italics are notes to myself--which problem is it?
Day 2 (Mon. Aug. 27) (Re) Read: Stemplot handout,
Section 1.1, rest of. Postpone
timeplots till we do SPSS. Read ahead, 1.2 thru p. 49.
Do to hand in: p. 25ff. See note below about stemplots, use
handout.
1.22 Make a stemplot (no histogram) & answer a,b
1.23 Use the applet (help here).
Find the dataset under the DataSets tab, then click the histogram tab. No
"Data Sets" tab? Try a different browser.
1.37 all: Truncate, don't round. Easiest to do (d) first and
then combine for b. (Don't bother to order them.)
1.38 Studytime--back to back
1.24 CO2 Use stemplot. Use stems 0,1,2,...(2|3 =
2.3) or 0*, 0t, 0f... (0|2 = 2, 1|9 = 19)
1.17 Make a dotplot, not a stem. |
Read, be
prepared to discuss
p. 94, 1.128 (leisure time)
p. 29, 1.15, 1.16 |
Optional |
Classroom changed permanently to Mac 121!
Introduce
yourself to your
neighbors--sides,
front & back. Check for Homework questions?
Handout: Stemplots
Honor code:
This community of learners is a rare and fragile thing. Trust is
the foundation of its structure. Betraying the trust damages the
whole community. Please do not betray my or your fellows' trust,
and I will do my best to reciprocate. The flip side of this is
that
if you do betray our trust, I will definitely pursue it in Community
Court. I want you to work together on homework and specifically
designated projects. Quizzes and exams are to be done
individually unless I tell you otherwise. Ask if you aren't sure!
Distribution of one
variable: what values, how many (or what proportion) of each.
"Make
Piles" -- Frequency table: count, percent="relative
frequency" (Hair color)
Graphical summaries of data: Area
represents proportion.
Categorical: Bar
or pie graph (Bar chart ordered by size = "Pareto chart")
Pie only ok if showing all categories (part of
whole) &
no overlap of categories.
Pie by hand? Template handout
last time
Quantitative:
Histogram.
Stem-and-leaf
(Stemplot). Dotplot
Counts or proportions = heights; Equal width bars on continuous
base ensures
"Area represents proportion."
Describing: Pattern-- and deviations from it
Shape (symmetric, or skewed (think smeared, or
sliding)
right or left),
(Humps: uni- or bi- modal (multi-) Two
humps
= two "causes"? M+F heights: hand around "living
histograms")
Some special shapes: uniform (flat) J-shaped
(p. 36 top left) bell-shaped (sec. 2.3)
Center, Spread (roughly now)
Outliers, gaps ? (different groups, sources?)
Histogram can change somewhat
depending on intervals you choose:
Moore Applet (
http://www.whfreeman.com/ips5e)
. or use disk in book) One Variable Statistical
Calculator, text pp. 14-15, IQ test scores
(Drag histogram bars R/L to change
"bins." No "Data Sets" tab? Try a different browser)
Handout: Stemplot (stem and
leaf) invented by John Tukey
!!Unordered first,!! then ordered if
necessary.
(Coarse, then fine sort is
Efficient way to put set in order--need for medians, next)
By tens, then
split?
Back
to back, comparing two groups. (or side-by-side on same
scale)
Not in text:
Stemplot, rounding when there are more than 2 decimal places?
Handout
says truncate (round down), Moore text does also. Some
sources
round to nearest. Tukey, the inventor, said truncate; throw away the
trailing
digits; I agree. This is supposed to be fast--rounding to
nearest
slows it down. I encourage truncating but you can do it either
way
and be right. If you truncate, your stemplot may look a little
different
from the text answers. (A stemplot is hard for a
computer
to do, but some packages do. For them, rounding to nearest is
easiest.
SPSS truncates, which is hard for a computer.)
Look at data from stats classes: ../StudatFall07.xls
Dotplot: Note bottom of p. 50,
fig.
1.19, use of a dot plot to display a data set of size
n
= 7. Just put a dot for every observation at its numerical place
on the axis. Stack them up if needed.
WHICH?
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?
Variability happens.
Things settle down on average, BUT conclusions are never certain.
Statistics gives us a
language
for talking about uncertainty.
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