Measures of Central Tendency: Mean

The most widely used measure of central tendency is the arithmetic mean. Commonly referred to as the "average," it is a concept that most students learn about in elementary school. The mean can be illustrated as follows:

By definition, the mean is the sum of the scores divided by the number of scores that entered that sum. In the example above, the data set includes the values {2, 2, 5, 6, 8, 9, 10}. The sum of these scores is (2 + 2 + 5 + 6 + 8 + 9 + 10) = 42. The number of scores in the data set is 7. Thus, the mean is equal to 42 / 7 = 6.

Expressed in terms of a formula, special notation called summation notation is used. The Greek capital letter sigma denotes "the sum of," and directs you to add a group of numbers. The capital letter X is used as a placeholder to represent any score for a particular variable in a given set of scores. The subscript indicates the specific score in the data set (e.g., X₁ is the score for person 1).