# James's Knowledge Graph

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 ($\sigma^2$)

$\sigma^2 = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n}$

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

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

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

$\sigma = \sqrt {\mu _2 }$

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 ### Averages: Measures of Central Tendency

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

The analysis of numerical data