The Measures of Central Tendency

and How to Apply Them

The Measures of Central Tendency are ways to look at the middle of a group of scores. These averages include the mean, median, and mode. Applying each of these descriptive statistics to your data has particular advantages.

The mean is the most commonly used measure of the middle. It is simply the arithmetic average. To find the mean, add up all of your scores (also called data points or values) and divide by the number of scores.

You would use the mean whenever you want to consider the values in your average--the mean student score in a class, or your average monthly heating bills. The mean is also the foundation of more powerful statistical tools.

Note that the symbol of the mean of a sample is X with a bar over it, but the mean of a population is represented by the Greek mu symbol.

Measures of Central Tendency

The median is the midpoint of a distribution of scores. To find the median, put the scores in order and find the middle point where they would "balance" if both sides were equal. Think of the median of a highway. Using the formula, the median position is n + 1 (the number of scores plus 1) divided by 2.

Use the median when you want to eliminate outliers that skew your distribution of scores. For example, you might want to find the median household income for a city so that the few billionaires don't raise the mean average income.

The mode is the most frequently occurring score. To find the most, simply look at your ordered scores and find the one (or ones) that appear most often. A distribution of scores may have more than one mode.

Use the mode when you want to find what "most people said" or which style of clothing was sold the most.

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