## Natural Resource Biometrics## Measures of DispersionMeasures of dispersion are used to describe the amount of scatter around the center of the distribution. They include range, mean deviation, variance, standard deviation, and coefficient of variation.
## RangeThis is simple the difference between the largest value and the smallest value. ## Mean deviationThis is the mean absolute difference of each observation and averaged. ## VarianceThe formula for the populations is different that the formula for the sample. Population variance is calculated as follows: Sample variance is estimated as follows: ## Computer FormulationThe formulations are much easier to use when calculating the these on a computer or calculator. In Excel® the buildin function: - =VAR.P(range of data)
- Example:
- =VAR.P( A1:A25 )
- Which will produce:
- Population variance for the data range
In Excel® the buildin function: - =VAR.S(range of data)
- Example:
- =VAR.S( A1:A25 )
- Which will produce:
- Sample variance for the data range
## Standard DeviationThe standard deviation is the square root of the variance. The population standard deviation can be calculated as follows: In Excel® the buildin function: - STDEV.P(range of data)
- Example:
- =STDEV.P( A1:A25 )
- Which will produce:
- Population Standard Devation for the data range
The sample standard deviation can be calculated as: In Excel® the buildin function: - =STDEV.S(range of data)
- Example:
- =STDEV.S( A1:A25 )
- Which will produce:
- Sample Standard devation for the data range
## Coefficient of VariationCoefficient of variation is a relative measure of dispersion that removes the units from the statistic. It can be calculated as:
## Standard ErrorBecause the variance on any sample will decrease with increasingn a
method of comparing samples of different size is need. This is Standard
Error for a sample and is given by:
Chapter 3 - Measure of Variability pages 35-46 in: -
**Phillips, J. L.**2000. How to think about statistics. W. H. Freeman and Co. New York. 202 pp. ISBN 0-7167-3654-3 -
**Zar, J. H.**2007. Biostatistical Analysis. Prentice-Hall, Inc. Englewood Cliffs, New Jersey. 718 pp.
Chapter 4 - Measure of Dispersion and Variability pages 27-32 in: |

Natural Resources Biometrics by David R. Larsen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License . Author: Dr. David R. Larsen Created: July 19, 1996 Last Updated: September 24, 2014 |