# 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:

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

**Document source**:
LexisNexis search for "JPMorgan dumps tradition",
or use the direct link here.
## 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

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
(you can use the FREQUENCY function to count the number below the average).
- 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 1a:
Excel
Basics.

Using Excel 1b:
Histogram and Regression.