Dispersion

Dispersion describes how spread out the values in a data set are around their centre, measured by the range, variance, standard deviation and coefficient of variation.

ByHoang TruongUpdated July 11, 2026

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Dispersion measures how spread out values are around their centre. Four branches' quarterly profits of €40,000, €48,000, €52,000 and €60,000 have a mean of €50,000 and a range of €60,000 − €40,000 = €20,000. Squaring and averaging the deviations from the mean gives a population variance of €52,000,000, and a standard deviation of roughly €7,211. Two data sets can share the same mean while carrying very different risk.

Where it fits

TopicDescriptive StatisticsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

R = X_{max} - X_{min}

Variables

$R$: Range (€)
$X_{ma x}$: Largest observation (€)
$X_{min}$: Smallest observation (€)

The simplest dispersion measure: the gap between the largest and smallest observations.

LaTeX

s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}}

Variables

$s$: Standard deviation
$x_{i}$: Each observation (€)
$\overset{x}{ˉ}$: Mean of the observations (€)
$n$: Number of observations

Measures the typical distance of individual observations from the mean, in the original units.

Check yourself

PracticeCORE

A company's quarterly profits over one year were €12,000, €18,000, €9,000 and €21,000. What is the range of these profits?

Select an answer to check your understanding.