Measures of Dispersion > Coefficient of Dispersion

## What is a Coefficient of Dispersion (COD)?

The term “coefficient of dispersion” can mean a few different things in statistics. **There isn’t one formula or definition that is universal. **Everything depends on the context of where you’re using the coefficient and what you want to do with it:

- Informally, some people use “coefficient of dispersion” interchangeably with
**“Coefficient of Variation”**. - The
**Karl Pearson Coefficient of dispersion**is simply the ratio of the standard deviation to the mean. - Green’s COD (C
_{x}) is suitable when dealing with densities. The formula is: sample variance/sample mean – 1/Σ(x-1). - As a measure of dispersion around a median, you can use the formula:

This is almost exclusively used to deal with property and market values. For solution steps, see*this New York State government sheet*. - The
**Quartile Coefficient of Dispersion**(see below), which is one of the more popular versions of COD found in research.

## What is a Quartile Coefficient of Dispersion?

The quartile coefficient of dispersion) is a measure of the spread of a data set. The formula is:

**Where**:

- Q
_{1}is the first quartile, - Q
_{3}is the third quartile.

The CoD tells you how spread out data sets are relative to each other. For example, if one data set has a CoD of 0.5 and another has a CoD of 0.10, then data set 1 is 5 times as great (0.5/0.10) as data set 2.

## Example

What is the quartile coefficient of dispersion for the following set of numbers?

2, 4, 6, 8, 10, 12, 14

Step 1 :**Find the 25th percentile (Q _{1}) and the 75th percentile (Q_{3}).** There are a few ways you can do this. One of the easiest ways is to use our interquartile range calculator. By hand, see: Finding Quartiles.

Plugging the data set into the calculator, we get:

- Q
_{1}= 25th percentile = 4 - Q
_{2}= 75th percentile = 12.

Step 2 :**Plug the numbers from Step 1 into the formula and solve: **

The coefficient of dispersion for this data set is 0.5.

**References**:

Bonett, D. G. (2006). Confidence interval for a coefficient of quartile variation. *Computational Statistics & Data Analysis. *50 (11): 2953–2957

Green, R. (1966). Measurements of non-randomness in spatial distribution. Res. Popul. Ecol. 8:1-7.

M. Kendall and A. Stuart, The advanced theory of Statistics, Vol. 1, 4th Edition, Charles Grifin and Co.

London, (1977).