# Variance: the square of the standard deviation. : Math « Development Class « Java

Variance: the square of the standard deviation.

```
import java.util.Arrays;

/**
* <p>Static methods for doing useful math</p><hr>
*
* @author  : \$Author: brian \$
* @version : \$Revision: 1.1 \$
*
* <hr><p><font size="-1" color="#336699"><a href="http://www.mbari.org">
* The Monterey Bay Aquarium Research Institute (MBARI)</a> provides this
* documentation and code &quot;as is&quot;, with no warranty, express or
* implied, of its quality or consistency. It is provided without support and
* without obligation on the part of MBARI to assist in its use, correction,
* modification, or enhancement. This information should not be published or
* distributed to third parties without specific written permission from
* MBARI.</font></p><br>
*
* <font size="-1" color="#336699">Copyright 2002 MBARI.<br>
*
*/

public class Util{
/**
* Variance: the square of the standard deviation. A measure of the degree
* of spread among a set of values; a measure of the tendency of individual
* values to vary from the mean value.
*
* @param values
* @return
*/
public static double variance(double[] values) {
double std = standardDeviation(values);
return std * std;
}
/**
* Standard deviation is a statistical measure of spread or variability.The
* standard deviation is the root mean square (RMS) deviation of the values
* from their arithmetic mean.
*
* <b>standardDeviation</b> normalizes values by (N-1), where N is the sample size.  This is the
* sqrt of an unbiased estimator of the variance of the population from
* which X is drawn, as long as X consists of independent, identically
* distributed samples.
*
* @param values
* @return
*/
public static strictfp double standardDeviation(double[] values) {
double mean = mean(values);
double dv = 0D;
for (double d : values) {
double dm = d - mean;
dv += dm * dm;
}
return Math.sqrt(dv / (values.length - 1));
//        double[] deviation = deviationFromMean(values);
//        double s = 0D;
//        for (double d : deviation) {
//            s += (d * d);
//        }
//        return Math.sqrt(s / values.length - 1);
}

/**
* Calculate the mean of an array of values
*
* @param values The values to calculate
* @return The mean of the values
*/
public static strictfp double mean(double[] values) {
return sum(values) / values.length;
}
/**
* Sum up all the values in an array
*
* @param values an array of values
* @return The sum of all values in the Array
*/
public static strictfp double sum(double[] values) {
if (values == null || values.length == 0) {
throw new IllegalArgumentException("The data array either is null or does not contain any data.");
}
else {
double sum = 0;
for (int i = 0; i < values.length; i++) {
sum += values[i];
}
return sum;
}
}
}

```

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