 # Coefficient of Dispersion

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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:

## 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:

• Q1 is the first quartile,
• Q3 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 (Q1) and the 75th percentile (Q3). 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:

• Q1 = 25th percentile = 4
• Q2 = 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).

CITE THIS AS:
Stephanie Glen. "Coefficient of Dispersion" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/coefficient-of-dispersion/
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