The mean is the mathematical average of a set of numbers. Using a mean to describe a score in a study tends to "smooth" the data to remove the influence of random errors in the experiment.
For example, perhaps you want to know how well students admitted to a local university score on the SAT. If you pull just one SAT score from the set of everyone accepted to the school, you may choose a student who got a perfect score. This would cause you to inaccurately conclude that everyone admitted to the university scored very high on the SAT. If, however, you took the mean score of all accepted students, the very high and very low scores would cancel one another out. The mean is a much better measurement of how well students perform on the SAT than using a single value.
The mean is calculated by adding all scores in a set and dividing by the number of scores included. You must include at least two scores to calculate the mean, but there is no maximum number of scores that you can use.
In psychology, the mean is reported in a very formulaic way, according to American Psychological Association (APA) style. State the finding of a particular test and write the mean score in parentheses. An italicized capital "M" should be used to represent mean, followed by an equals sign and the average score. For example, "Admitted students to the local university scored higher than the national average (M = 1,430)."
In psychology, no conclusion can be drawn about differences between two means. One group may have a higher mean than another, but the difference may not be statistically significant. More complicated tests must be performed to make conclusions based on differences between two or more means.
The statistical mean may not be the best measurement of central tendency if data is strongly skewed. Income is a good example of a skewed distribution. Most people make less than $80,000 per year, but a few make several million dollars annually. Taking the mean income of everyone in the United States results in high value because of the few millionaires who skew the data. Although this value is the true mean, it may not be the best way to describe the amount of money most Americans make.
Other measurements of central tendency may be used in place of the statistical mean in psychological research. The median is the middle value in a set of data. This is a more appropriate measurement when data is strongly skewed (as in the income example above). The mode or most common value is also sometimes used to describe a set of data.