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# Measures of Central Tendency and Dispersion

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## 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. Examine the following measures of central tendency for the salaries of all the players in the Major League Soccer (MLS), the highest level for professional soccer in the United States and Canada, in the 2011-2012 season.

1. The median salary for aMajor 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 median tells us that half of the salaries in the MLS are above$87,862.50 and half of the salaries are below $87,862.50. In other words$87,862.50 is in the middle of all the MLS salaries.
2. 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 mean salary tells us that on average a MLS player makes$147,693. If all the salaries of all the MLS players were combined and redistributed evenly, then every player would make $147,693. 3. 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 mode tells us that the most common salary of a MLS player is $34,000. 4. 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)? The range tells us that the difference between the lowest and highest salary of a MLS player is $6,479,900. This shows how different the salaries are. 5. Which of the measures of central tendency (mean, median, mode, and range) are the most useful for analyzing the salaries of MLS players? Explain. The median and range are very useful for analyzing this data. The median indicates where the data is split, and subsequently where each half the data falls. The range shows how spread out this set of data is. Mode is also useful as it indicates that$34,000 is the most common salary of a player, and it is a lower salary than the other measures of central tendency.

### Extension Investigation

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

1. For what kinds of data is the median the most useful? Explain. The median is most useful for sets of data that are skewed, as it will indicate where the data is split in half. So, even though it is skewed it will tell you where the middle value is.
2. For what kinds of data is the mean the most useful? Explain. The mean is most useful for sets of data that are evenly distributed,symmetrical and doesn’t have outliers (extreme values).
3. For what kinds of data is the mode the most useful? Explain. The mode is most useful for sets of data that vary, it is not useful when all the values are the same.
4. For what kids of data is the range the most useful? Explain. The range is the most useful for sets of data that have a big range, as it indicates how spread out a set of data is and indicating where the outliers are.

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.

### 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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