Although the range is easy to compute, it can provide a misleading impression of a distribution's variability when outliers are present. Because the range relies solely on the absolute highest and lowest values, a single extreme score will drastically inflate the range, giving the false appearance that the entire dataset is widely spread out.

Sensitivity of the Range to Outliers

To calculate the range of a distribution, subtract the lowest score from the highest score. For example, if the highest score in a dataset is $$24$$ and the lowest score is $$15$$, the range is calculated as $$24 - 15 = 9$$.

Example of Calculating the Range

Which measure of variability is calculated as the difference between the highest and lowest scores in a distribution?

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

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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

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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

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.

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