# Dispersions: Measures of spread

A **dispersion** is a statistical method to summarize the spread, as opposed to central tendency, of a set of numerical data. The primary types of dispersion are range, variance, and standard deviation.

## Range

**Range** is the difference between the maximum and minimum value in a set of numbers.

## Variance ($\sigma^2$)

**Variance ($\sigma^2$)** is the mean of the squared differences of each data point from the mean of the full dataset. To calculate variance:

- Find the mean of the data
- Subtract the mean from each number in the dataset, then square the result (to make it positive).
- Find the mean of the squared differences

## Standard Deviation ($\sigma$, $STD$)

Standard deviation ($\sigma$ or $STD$) is the square root of the variance. If a standard deviation is low, the values tend to be close to the mean. If the standard deviation is high, the values tend to be spread out.

## Deeper Knowledge on Dispersions: Measures of Spread

### Averages: Measures of Central Tendency

Usage and calculations for mean, median, and mode on a set of numbers

### Interquartile Range (IQR)

How to find the interquartile range (IQR) of a number collection

## Broader Topics Related to Dispersions: Measures of Spread

### Averages: Measures of Central Tendency

Usage and calculations for mean, median, and mode on a set of numbers

### Statistics

The analysis of numerical data