Unit 3: Variation and the Normal Curve
Text reading and review exercises:
Review Chapters 5 and 6 of FPP and do the following review exercises:
Chapter 5 [pages 93-95]: 1, 2, 3, 8, 9, 11
Chapter 6 [pages 104-105]: 4, 5
Special Review Exercises [pages 105-108]: 9, 10, 13
Reading:
"Buff Your Brain",
by Sharon Begley, The Daily Beast, 1 Jan 2012. A version
of this article appeared as the cover story in Newsweek,
Jan 9 and 16, 2012.
Document source: Linked to
The Daily Beast
website.
Possible essay questions:
- What does the article advocate as the best ways to increase IQ?
- How does the possible change in IQ mentioned in the article relate
to the differences (of up to 15 points) between average IQs of
Americans of various racial backgrounds?
Computer project
This week we work with salary data for 2011 Major League Baseball players.
Preliminary Writeup
Before you do any computations with a spreadsheet, what percent
of the players do you expect to have below-average salaries? And what
percent of the players do you expect to have salaries below the median? Do
you expect the data to be normally distributed?
Now, suppose the data is normally distributed. What percent of the players
would have salaries below the 70th percentile? What value would
the 70th percentile be for a normally distributed dataset with
average $3.30 million and an SD of $4.53 million?
On the Computer
Copy the 2011 baseball salary data below into a spreadsheet program:
2011 Baseball salaries
(salaries-only list): Move these into the spreadsheet.
Baseball
salaries: More details from the source, if you are interested (but
you don't need them).
- Create a histogram for the data using class intervals of length $2,000,000,
up to $32,000,000.
- Compute the value of the average, median, mode, 70th percentile
and standard deviation for the salaries. (The Excel function for what we
call SD is "stdevp" [the "p" stands for population]. The function "stdev"
gives what we will later in the course call "SD+", the "sample
standard deviation". The Excel "percentile" command requires two arguments,
first the location of the list of numbers and second the desired percent,
in the form .7 rather than 70.) (An Open Office spreadsheet will do very
similar things, but the Frequency command must be entered using the
Insert->Function menu; and the Percentile command wants its second argument
in the form 70%.)
- Determine the percentage of players that have below-average salaries.
- Compare the actual data with your predictions. Is salary data for baseball
players approximately normally distributed?
- Create an accurate one- or two-sentence summary of the salary data suitable
for a newspaper article. When you state the value of a statistic, explain
to your reader how it should be interpreted.
- Create a misleading summary of the data using the value of at least
one TRUE statistic.
If you have trouble with the spreadsheet program, consult the supplement
Using Excel 1:
Excel
Basics.
Last revised: 27 January 2012. Mail to
dlantz@colgate.edu
Copyright 2012 © Colgate University. All rights reserved.