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:

Reading between the (noble) lies, by Phil Brand, The Washington Times, September 7, 2008, Books section, M28.

For whom the bell curve tolls; students vary widely in academic ability, but we pretend everyone can be above average, by Margaret Wente, The Globe and Mail (Canada), September 6, 2008, Comment column, page A25.

Document source: LexisNexis.

Possible essay questions:

These are both largely favorable reviews of the same book. In a reasonably short space (say, a page) describe the mindset (or "noble lie", or whatever it is) that the book and these article criticize and how it affects public education.
One of the reasons advanced for public education is to have a more informed electorate. How do the authors adress this goal of public education, and how do you feel they should address it?
(Extra credit) Both articles mention "Lake Wobegon". Why?

Computer project

This week we work with salary data for 2002 Major League Baseball players.

Preliminary Writeup
Before you do any computations with Excel, 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 70^th percentile? What value would the 70^th percentile be for a normally distributed dataset with average $2.387 million and an SD of $3.067 million?

On the Computer
Copy the 2002 baseball salary data below into a spreadsheet program:
2002 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 $1,000,000, up to $20,000,000.
Compute the value of the average, median, mode, 70^th 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.)
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.