The mathematical formula for the mean differs slightly depending on whether you are referring to the sample mean or the population mean:

Sample mean: where: (read as 'x bar') is the mean of the set of x values. is the sum of all the x values, and n is the number of data values in the sample.

Population mean: where: (read as 'x bar') is the mean of the set of x values. is the sum of all the x values, and N is the number of data values in the population.

We calculate the statistical mean of a list of numbers in order to find the general tendency of the numbers in the list.

Characteristics of the mean:

• Every value in the distribution contributes to the value of the mean.
• 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.
• Arithmetic mean is affected by change of both origin and scale. (Proof)
• Its value may not actually exist in the data (e.g., for the data set 2,3,4 and 5; the mean is 3.5).

Remember that the word average means only the one measure that best represents a set of scores, and that there are many differents types of averages. Which type of average you use depends on the question that you are asking and the type of data you are trying to summarize.

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