Unit 3: Variation and the Normal Curve

Text reading and review exercises:

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.

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

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 70^th percentile? What value would the 70^th 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).

1. Create a histogram for the data using class intervals of length $2,000,000, up to $32,000,000.
2. 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.) (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%.)
3. Determine the percentage of players that have below-average salaries.
4. Compare the actual data with your predictions. Is salary data for baseball players approximately normally distributed?
5. 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.
6. Create a misleading summary of the data using the value of at least one TRUE statistic.

Last revised: 27 January 2012. Mail to dlantz@colgate.edu
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