  # Relative Dispersion / Absolute Dispersion

## What are Absolute Dispersion and Relative Dispersion?

Absolute & relative dispersion are two different ways to measure the spread of a data set. They are used extensively in biological statistics, as biological phenomena almost always show some variation and spread.

The easiest way to differentiate relative dispersion/absolute dispersion is to check whether your statistic involves units. Absolute measures always have units, while relative measures do not.

## Absolute Measures of Dispersion

Absolute measures of dispersion include:

Absolute measures of dispersion use the original units of data, and are most useful for understanding the dispersion within the context of your experiment and measurements.

## Relative Measures of Dispersion

Relative measures of dispersion are calculated as ratios or percentages; for example, one relative measure of dispersion is the ratio of the standard deviation to the mean. Relative measures of dispersion are always dimensionless, and they are particularly useful for making comparisons between separate data sets or different experiments that might use different units. They are sometimes called coefficients of dispersion.

## Some Commonly Used Measures of Relative Dispersion / Absolute Dispersion

The simplest measure of absolute dispersion is the range. This is just the upper limit minus the lower limit; the largest data point minus the smallest. We can write this as R = H – L.

For example, if a data set consisted of the points 2, 4, 5, 8, and 18, the range would be 18 – 2 = 16.

The analogous relative measure of dispersion is the coefficient of range. This is given by (H – L)/(H + L). For our example data set, it would be the ratio (18 – 2)/(18 + 2), so (16/20) or 4/5.

The standard deviation is a more complicated measure of absolute dispersion, you could calculate it by squaring the difference between each data point and the mean, summing those squares, dividing by a number that is one less than the number of your data points, and then taking the square root of that. Since your values are squared and in the end the square root is taken again, the standard deviation is given in the your original units of measure.

The coefficient of standard deviation, the analogous measure of relative dispersion, is just the standard deviation divided by the arithmetic mean. To give it as a percentage rather than a ratio, multiply by 100%.

## References

Sharma, Ananya. Absolute Measures of Dispersion. Retrieved from https://www.slideshare.net/AyushiJain134/absolute-measures-of-dispersion on August 11, 2018.
Sharma, Ananya. Measures of Dispersion in Statistics. Retrieved from https://www.slideshare.net/tanvigarg90834/chapter-11-measures-of-dispersionstatistics on August 11, 2018
Measures of Dispersion: Departures of Scores from Central Tendency. Virginia Tech. Updated September 3, 1998. Retrieved from https://simon.cs.vt.edu/SoSci/converted/Dispersion_I/activity.html on August 11, 2018.

------------------------------------------------------------------------------

Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!

Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.