Math 151 , Day 5 Wed., Feb.6, Spring '08 .After class. Hit reload to get most current version
HW Day 5: (Re)Read Ch.2 thru p. 47 Check: 2.15,17,18
(5#summary/boxplot). Read 53-55, "Organizing...".. New: pp.47-50-
standard
deviation, Check 2.19(don't calculate. It's not #a), 20, 21,
22.
PLEASE read ahead in Ch.3,
64-9 density curves, & ahead
Normal
Distributions 70-84:
There's a lot there, and I will cover a good chunk Friday.
Hand
in:
(quartiles, 5#summary etc. repeated
from Day 4, + a couple)- - -
p. 58, 2.29 fruit eating
p. 58, 2.30 newborns. (I said I wouldn't
make you make a histogram, but the data's already pre-binned, so do it
here.) Also Describe the distribution--symmetric, skewed?
p. 58, 2.28 U.
endowments. They mean, what do you have to count in to, in
the list, to locate the mean and quartiles?
p. 59, 2.34 guinea pigs
survival: For a) use the One Variable Statistical Calculator
Applet at http://bcs.whfreeman.com/bps4e
or on your text's CD (If you have an older, used book, it may
be in the datasets as if for BPS3e; ex02-23.dat).
Just observe the skewness. For b), find the 5-number summary
(easy since they're in order in the book), check your answers with the
Applet results. Draw the boxplot and compare with the histogram
on your screen. (with or without outliers, I don't care.)
p. 45, 2.5 Wood again. Go ahead and
use the stemplot figures to find the quartiles. Also make a
boxplot.
p.58, 2.27 Flower length: Find the 5-number summary for bihai,
from the stemplot p. 55. If you want more practice, do the other 2 by
hand also, but you may just use the numbers from the answers in the
back of the book. Use them to make 3 side by side boxplots, and
finish the problem as written.
A. You are driving on the thruway from Syracuse to Rochester and
keep track of how many vehicles you pass and how many pass you.
You find that these 2 numbers are the same. Your speed on the
thruway is: (a) the Mean speed of the cars, (b) the Median speed of the
cars, (c) the Modal speed of the cars. Choose one, and justify
your choice.
p. 60, 2.35 days of births, Canada The
book's question is very open-ended. Answer instead the questions
just below the box*
p.55, 2.12 Rainforest logging. Use
the
4-step process, see below, p. 53-5&/or inside
front cover.
Note that "state", the first step, is usually "done"=the textbook
statement of the problem. The data are probably suitable for
mean& standard deviation, but we don't have the SPSS power to do
them easily yet, so use your hand methods--stemplots, quartiles,
boxplots... This is one where working together with others can
have real benefits, since it's pretty open-ended.
Postpone the rest: Standard deviation
B. Find the mean and standard
deviation of these 4 numbers: 2, 2, 4, 8 by hand.
p. 50, 2.9 Blood phosphate Do a and b by hand. Use
SPSS or some other tool**
to do c. Write your answers from screen to paper.
Also (re)make a dotplot of the data, mark the mean with a wedge, and
indicate the standard deviation s with <----> lines from
the mean to both sides, s long. (like the sketch below)
p. 51, 2.10 xbar=7.50, s = 2.03
the same for both dist's. Don't do the calculations--just make
stemplots & compare their shapes!
ALSO, type the data for Dataset B into SPSS or other**,
excluding the outlier of 12.50. Find and write down the mean and
s.d. now. Compare to xbar=7.50, s
= 2.03 .
|
Read, to discuss
|
Optional
p. 62, 2.40, 2.43 Play with summary numbers. Use the
Applet, One variable statistical calculator; type data in at the Data
tab.
|
* Questions for 2.35, p. 60:
A. a) Which
day had the lowest Median (and about what was that number)?
b) Which
day had the highest Median (and about what was that number)?
c) Which day had the highest variability (spread), measured by:
--IQR (about what are the quartiles for this day)?
--Range (about what are min and max for this day)?
d) Tuesday appears to be somewhat skewed.
Left, or Right skewed?
B. Compare the Canadian with the American data (p. 10, 1.4):
a) Is the general pattern the same in the Canadian and American
data? Discuss briefly the common findings.
b) (Following the 4-step method, p. 53:) State the issue:
Is the weekend/weekday difference greater in Canada or the US (or are they similar?)
Formulate an appropriate answer: In both countries, Tuesday is highest,
Sunday is lowest. Relate the number of Tuesday's births to the number of Sunday's
births for each country. Proportion/ percents will show the relationship
best, since there are different types of numbers for the two countries.
Solve: For Canada,you have (part A) estimated the median number
of births for Tuesday and also for Sunday, from the graph. Take the number
for Sunday, divide by Tuesday's number, restate as a percent. For U.S., use
the numbers on p. 10, dividing Sunday by Tuesday. Conclude, something
like this: " In Canada, on Sunday(s), the number of Sunday births was
___% of the number of births on Tuesday. In US (the parallel statement.)
Therefore the difference is greater(?) in (Canada?US?). This may indicate
that proportionately more planned births occur in (Canada?US?).
c) The picture for 2.35 makes the difference between
weekdays and weekend days look more extreme than it actually is. Why/how?
d) To make the numbers more comparable, (U.S.
total of all births in a year of Sundays/Tuesdays, Canada median number per
Sunday/Tuesday) it would be better if we had the Canadian Means. (because
mean times n = total). Look at the boxplots and tell whether the Canadian
mean for Tuesday would be less than the median, about the same, or more than
the median. Do the same for Sunday.
(Postpone)**Where
it says to use SPSS, you may use SPSS
(preferred) (Didn't get handout? Link Download
shows correct image), or a statistical calculator if you have one, or the Applet,
One Variable Statistical Calculator, on the web
http://bcs.whfreeman.com/bps4e
or on the CD in your book.
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Class Email: Math151@wells.edu. Email me if you didn't get the
notice yesterday. Use to ask questions (esp. "is this problem written
wrong?"), look for co-studiers, etc. I'll use to send notices, corrections,
etc.
Math Clinic General schedule should be posted
on the door outside Mac 120 soon; online soon?
Mallory Burch Wed. 7-9 pm, Thurs. 6-9 pm
Matthew Peddle: M 1:30-3:30, F 1:30-3:30
Handouts today: SPSS--Mean and SD
We'll have a whole day on SPSS, in the computer lab, Monday.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - -
Homework questions? Mean/Median
review Day 3
Continuing with Quartiles, five number summary, boxplot, IQR. Notes
Day 3
Start here next time:
Summaries
of Middle & Spread continued--"Systems:"
-- (Midrange, Range Very
sensitive to outliers--they use only the max and min!)
-- Median, IQR (+ Quartiles
Q1, Q3, 5-number summary), based on percentiles (j'th percentile is > j% of the data)
-- Mean, StandardDeviation "y-bar"
(or "x-bar"), "s" (good for symmetric unimodal, no outliers)
Standard
deviation
(measure of Spread that goes with mean)
Variance s2:
(almost) average
of squared deviations from the mean.
(Divide by (n-1)
"degrees of freedom")
s :
Standard deviation is the square
root of
the
variance.
Computation: I will require you to know how to do it by hand for
4 or 5 observations
(see BPS4e p. 48-9 for formula & computation example.
)
Demo: 1,1,2,4, mean = 2, sum of squared deviations
= 6, variance = 2, s = 1.41
1,1,2,4,12, mean = 4, sum of squared deviations = 86, variance =
21.5, s = 4.64.
(Midcomputation check: Sum of deviations from the mean (before
squaring
each) always = 0 )
--s is Always > 0 (0 only if all observations are =)
--s units the same as those of the
observations
(squared and squarerooted).
Physics: angular momemtum (spinning ice skater)
Not so weird: High school geometry?
Remember
Pythagorean theorem: c2
= a2 + b2:
hypotenuse of right triangle is also square root of a sum of squares.
Very
sensitive
to outliers (the outliers contribute much more than their
share to the Sum of
Squared Deviations from the Mean)
Mean and Standard Deviation are for
Symmetric
Unimodal distributions without big outliers.
(ideally "Bell-shaped" = Normal)
SPSS, for simple computation: Handout
Organizing a
statistical problem:
Four-step process (pp. 53-5, & inside front
cover)
State: the issue to be explored, question to be addressed
(real-world) (In hw problems, often already stated.)
Formulate: What statistical tools, measures,
analyses should we use to answer the question?
Solve: Carry out the process. (May need to
back up & try again. Decide on mean, s.d., but stemplot shows
badly skewed? go back and decide on 5#summary instead.)
Conclude: Give the conclusion as it addresses the
real-world question/issue.
Any time left??: Begin p. 55, 2.12 in class
in pairs
(or 3's). Decide what analyses to do; start doing them (make a
copy for each)
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