Mean

Fundamentals of Social Statistics

 

The mean (symbolized  “X -bar” and sometimes M as a sample statistic, or μ as a population parameter) is the average that is the “balance point” in a distribution.  It is calculated by adding up (summing) all of the scores and dividing by the number of scores (n).  The mean provides researchers with a way of finding the most typical value in a set of scores.

Computing the Mean

Compute the mean using the following formula:

Mean Formula

Where:

·        X-bar  is the mean of X

·          ΣX is the sum of the X values

·          And N is the number of elements

In a skewed distribution, the mean will be “pulled” toward the outliers.  That is, the mean is sensitive to extreme scores.  The more extreme the outliers are, the less useful the mean is as a measure of central tendency.  When extreme scores will influence the mean too much, it should be abandoned in favor of a statistic that does not use every value in the distribution and thus is not biased by extreme scores.

The mean is the most widely used measure of central tendency, but it can give deceptive results if the data contain any unusually large or small values, known as outliers.

An important characteristic of the mean is that it is the “balance point” of the distribution.  This means that it is the point at which the differences between every other score and the mean sum to zero.  This may not seem very important now, but the importance of it will be more important later when we discuss measures of variability such as the standard deviation and variance.

The mean is an appropriate measure of central tendency when:

-The data are measured at the interval or ratio level

-The data are approximately normally distributed


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Last Modified:  02/18/2019

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