Unit 3: Variation and the Normal Curve

Text reading and review exercises:

Reading:

JPMorgan dumps tradition: Firm creates a new asset allocation tool that embraces 'fat-tail' events Pensions and Investments, May 4, 2009.

Possible essay questions:

• What does "embracing fat tail events" have to do with the normal distribution?
• Why might analysis of fat tails protect against events such as the market crash of 2008?
• Why do many investor models use the normal distribution?

Computer project

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).

1. Create a histogram for the data using class intervals of length $1,000,000, up to $20,000,000.
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.)
3. Determine the percentage of players that have below-average salaries (you can use the FREQUENCY function to count the number below the average).
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.