Mean

The mean is the most often-used measure of central tendency and is usually defined as the sum of all the scores in a data set divided by the number of observations. It can also be defined as the point about which the sum of the deviations is equal to zero.

The formula for the computation of the mean is as follows:

where

• The letter X with a line above it (also called “X bar”) is the mean value of the group of scores or the mean.
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• The Σ, or the Greek letter sigma, is the summation sign, which directs you to add together what follows it.
• The X is each individual score in the group of scores.
• n is the size of the sample from which you are computing the mean.

For example, the following data set in Table 1 consists of 30 cases with two variables, reaction time and accuracy, two measures often used in research on cognition and learning.

To compute the mean, follow these steps:

• 1.
  List the entire set of values in one or more columns such as you see in Table 1. These are all the Xs.
• 2.
  Compute the sum or total of all the values.
• 3.
  Divide the total or sum by the number of values.

Applying the formula you see above to the sample data results in the following two means:

The mean is sometimes represented by the letter M and is also called the typical, average, or most central score.

One should keep in mind the following about the mean:

• The sample mean is the measure of central tendency that most accurately reflects the population mean.
• The mean is like the fulcrum on a seesaw. It is the centermost point where all the values on one side of the mean are equal in weight to all the values on the other side of the mean. That's why the sum of the deviations about the mean always must equal 0.
• The mean is very sensitive to extreme scores. An extreme score can pull the mean in one or the other direction and make it less representative of the set of scores and less useful as a measure of central tendency. This is the argument for using the median as a measure of central tendency.