Statistical dispersion

In statistics, dispersion, also called variability, scatter, or spread, describes how much a group of numbers is stretched out or squeezed together. It helps us understand how different the values in a set are from each other. For example, if the numbers are very different, we say the dispersion is large. If they are very similar, the dispersion is small.

Common ways to measure dispersion include variance, standard deviation, and interquartile range. These tools help scientists and mathematicians describe data more clearly. When the variance is large, the data points are spread out. When the variance is small, the data points are close together.

Dispersion is different from central tendency, which tells us about the middle or average of the data. Both dispersion and central tendency are important for understanding how numbers are arranged in a distribution.

Measures of statistical dispersion

A measure of statistical dispersion is a number that shows how spread out data is. If all the data is the same, this number is zero. The bigger the number, the more the data is spread out.

Some common measures of dispersion include:

• Standard deviation
• Interquartile range (IQR)
• Range
• Mean absolute difference (also known as Gini mean absolute difference)
• Median absolute deviation (MAD)
• Average absolute deviation (or simply called average deviation)
• Distance standard deviation

These measures are often used to understand how data changes with different scales. Other measures, like the coefficient of variation and quartile coefficient of dispersion, do not have units, even if the data has units. There are also special measures for certain purposes, like the Allan variance for dealing with noise.