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Measures of dispersion are descriptive statistics that describe how spread apart or dispersed the scores in a distribution are. Common examples of these measures include the range, standard deviation, and variance.

Measures of Dispersion

An example of variability can be observed when comparing two distributions that share the same central tendency (e.g., a mean, median, and mode of $$10$$) but differ in their spread. In a distribution with relatively low variability, all scores are clustered close to the center. Conversely, in a distribution with relatively high variability, the scores are spread across a much greater range.

Example of Variability in Distributions

The range is a straightforward measure of variability calculated as the difference between the highest and lowest scores in a distribution.

Range

The variance, symbolized as $$SD^2$$, is a measure of variability defined as the mean of the squared differences between each score and the distribution's mean. While variance is a foundational measure in inferential statistics, its square root—the standard deviation—is typically used in descriptive statistics.

Variance

The standard deviation is the most widely used measure of variability, representing the average distance that individual scores within a distribution deviate from the mean.

Standard Deviation

What do measures of dispersion primarily describe within a dataset?

If a researcher finds that all participants in a study receive the exact same score on a memory test, the measures of dispersion for this distribution will be zero.

A researcher is calculating the standard deviation to describe the spread of scores in a psychology experiment. Arrange the steps of this calculation in the correct logical order, from the first step to the final result.

A researcher is analyzing the spread of scores in various psychological studies. Match each data scenario with the specific impact it will have on the measures of dispersion for that distribution.

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