Measures of Central Tendency
Measures of Central Tendency
Measures of Central Tendency
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Natural Resource Biometrics July 19, 2000 oak.snr.missouri.edu/nr3110/<br />
s<br />
2<br />
<br />
n<br />
<br />
i1<br />
x<br />
2<br />
i<br />
n<br />
<br />
<br />
x<br />
i1<br />
<br />
n<br />
n 1<br />
2<br />
<br />
<br />
<br />
i<br />
Standard Deviation<br />
The standard deviation is the square root <strong>of</strong> the variance. This statistics in the units <strong>of</strong> measurement. The population<br />
standard deviation can be calculated as follows:<br />
<br />
n<br />
<br />
i1<br />
x<br />
2<br />
i<br />
<br />
<br />
<br />
<br />
N<br />
n<br />
<br />
i1<br />
x<br />
N<br />
<br />
<br />
<br />
i<br />
2<br />
The sample standard deviation can be calculated as:<br />
s <br />
n<br />
<br />
i1<br />
x<br />
2<br />
i<br />
n<br />
<br />
<br />
x<br />
i1<br />
<br />
n<br />
n 1<br />
2<br />
<br />
<br />
<br />
i<br />
Coefficient <strong>of</strong> Variation<br />
Coefficient <strong>of</strong> variation is a relative measure <strong>of</strong> dispersion that removes the units from the statistic. It can be calculated<br />
as:<br />
Standard Error<br />
s<br />
s<br />
cv cv 100<br />
x<br />
x<br />
Because the variance on any sample will decrease with increasing n a method <strong>of</strong> comparing samples <strong>of</strong> different size<br />
is need. This is Standard Error for a sample and is given by:<br />
2<br />
s<br />
s x<br />
<br />
n<br />
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License. 2<br />
Author: Dr. David R. Larsen
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