## Usefulness of Mean, Median, Mode and Range

### Topic

When is it most useful to use the mean, median, mode or range?

### Vocabulary

- Median
- Mean
- Mode
- Range
- Measures of Central Tendency

### Student Exploration

#### When is it useful to use the Median? When is it useful to use the Mean? Mode? And Range?

Soccer Player.

In statistics we have many different measures of central and it can be different to determine which method of measure is the most useful.

- The median salary for a Major League Soccer (MLS) player is $87,862.50. The MLS is the highest level of professional soccer in the United States and Canada. What does the median tell us about the salaries of all the MLS players (the entire set)?
- The mean salary for a MLS player is $147,693. What does the mean tell us about the salaries of all the MLS players (the entire set)?
- The mode salary for a MLS player is $34,000. What does the mode tell us about the salaries of all the MLS players (the entire set)?
- The range salary for a MLS player is $6,479,900. What does the range tell us about the salaries of all the MLS players (the entire set)?
- Which of the measures of central tendency (mean, median, mode, and range) are the most useful for analyzing the salaries of MLS players? Explain.

### Extension Investigation

The following are extension questions about the usefulness of the measures of central tendency.

- For what kinds of data is the median the most useful? Explain.
- For what kinds of data is the mean the most useful? Explain.
- For what kinds of data is the mode the most useful? Explain.
- For what kids of data is the range the most useful? Explain.

Research the salaries of players in the United European Football Association (UEFA). Determine the measures of central tendency (Mean, Median, Mode, and Range) for the UEFA. What measure of central tendency is the most effective for analyzing the salaries for the UEFA players? Explain.

Research the salaries of the soccer players in a different soccer/football association, maybe in your own country if you do not live in the United States or Europe. Determine the measures of central tendency (Mean, Median, Mode, and Range) for that soccer/football association. What measure of central tendency is the most effective for analyzing the salaries for the players in that association? Explain.

### Resources Cited

http://www.altiusdirectory.com/Sports/mls-salaries.php

### Connections to other CK-12 Subject Areas

- Median of Large Sets of Data
- Measures of Central Tendency and Dispersion
- Mean
- Mode

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