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# Measures of Central Tendency and Dispersion

## Mean, median, mode, range

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What Does It All Mean?

In the United States, people are expected to pay taxes on income earned over the course of the year in order to create funds for federal programs: K-12 education, highway maintenance, NASA’s space exploration, disaster relief, and more. But, would you want everyone to pay the same tax rate (percent of their income)? Would you want the tax rate to be based on the mean, median, or mode income? What tax rate is the most fair for everyone?

#### Why It Matters

The median household income in 2004 in the United States was $39,000 (for those ages 25-54) and the mean was approximately$60,000. Why is there such a big difference? The mean is strongly affected by very high incomes. In the United States, the upper class consists of only 1% of the population and these people have a household income of at least \$250,000. This very small percentage of people with very high incomes increases the mean income of the population. The median, on the other hand, is not affected by those very high incomes.

In order to try and achieve equity with taxes, the U.S. has divided earners into tax brackets. For an individual or household, the more money earned, the higher your tax bracket and the more taxes you will have to pay. The brackets are determined by median income, the poverty line, and other factors that change annually with the latest population data.

See for yourself: http://en.wikipedia.org/wiki/Income_tax_in_the_United_States

#### Explore More

Imagine that you’re the principal of your high school and that you’ve decided to host a pizza party for the class that does the best on the upcoming math exam. Which measure of central tendency (mean, median, or mode) would you use to determine which class gets the pizza party?

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