# Variance and Covariance

## How Much Money Do Baseball Players Really Make?

It is commonly accepted today that most baseball players make millions of dollars and that most of them are not worth it. In fact, the average (mean) salary of a ballplayer in the majors leagues is \$1.2 million dollars. Only given this fact, it is easy to see how the perception of the overpaid baseball player was created.

However, it is often conveniently ignored that the median salary for major leaguers is only \$410,000. Remember, that the median is the middle salary for baseball players. This means that 50% make more than \$410,000, but 50% make less.

That's still a lot of money but does not justify the perception that America has on major league salaries. So we are still stuck with the question if the salaries for the majority of baseball players are consistent with the public belief that they make too much money.

Another statistic, besides the mean and median, that can help us answer this question is called the variance. The variance is a measure of the spread of data.

The following lesson will help you explore the idea of variance and how it is used in statistics. The lesson should be done in the order presented below.

The above statistics are from George Will, Washington Post, Sunday, Sept. 4, 1994, page C7

Note to instructors: Please read the Teacher's Commentary for a synopsis of the lesson, suggestions on how to use it and its links to the NCTM standards.

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