### 如何确定一组值的标准偏差（stddev）？

#### 12 个答案:

``````public static double StandardDeviation(List<double> valueList)
{
double M = 0.0;
double S = 0.0;
int k = 1;
foreach (double value in valueList)
{
double tmpM = M;
M += (value - tmpM) / k;
S += (value - tmpM) * (value - M);
k++;
}
return Math.Sqrt(S / (k-2));
}
``````

＆＃34;虽然平方和算法在大多数情况下工作正常，但它   如果您正在处理非常大的数字，可能会造成大麻烦。您   基本上可能会出现负差异＆＃34;

``````    public static double StandardDeviation(double[] data)
{
double stdDev = 0;
double sumAll = 0;
double sumAllQ = 0;

//Sum of x and sum of x²
for (int i = 0; i < data.Length; i++)
{
double x = data[i];
sumAll += x;
sumAllQ += x * x;
}

//Mean (not used here)
//double mean = 0;
//mean = sumAll / (double)data.Length;

//Standard deviation
stdDev = System.Math.Sqrt(
(sumAllQ -
(sumAll * sumAll) / data.Length) *
(1.0d / (data.Length - 1))
);

return stdDev;
}
``````

Math.NET库为您提供了这个功能。

PM＆GT;安装包MathNet.Numerics

``````var populationStdDev = new List<double>(1d, 2d, 3d, 4d, 5d).PopulationStandardDeviation();

var sampleStdDev = new List<double>(2d, 3d, 4d).StandardDeviation();
``````

Jaime接受的答案很棒，除非您需要在最后一行中除以k-2（您需要除以“number_of_elements-1”）。 更好的是，从0开始k：

``````public static double StandardDeviation(List<double> valueList)
{
double M = 0.0;
double S = 0.0;
int k = 0;
foreach (double value in valueList)
{
k++;
double tmpM = M;
M += (value - tmpM) / k;
S += (value - tmpM) * (value - M);
}
return Math.Sqrt(S / (k-1));
}
``````

``````public static double StandardDeviation(List<double> valueList)
{
if (valueList.Count < 2) return 0.0;
double sumOfSquares = 0.0;
double average = valueList.Average(); //.NET 3.0
foreach (double value in valueList)
{
sumOfSquares += Math.Pow((value - average), 2);
}
return Math.Sqrt(sumOfSquares / (valueList.Count - 1));
}
``````

``````cnt = 0
mean = 0
meansqr = 0
loop over array
cnt++
mean += value
meansqr += value*value
mean /= cnt
meansqr /= cnt
``````

``````sigma = sqrt(meansqr - mean^2)
``````

BTW--对`Average`Demi答案中数据的第一次传递隐藏在对{{1}}的调用中。这样的事情在一个小清单上肯定是微不足道的，但如果列表超过缓存的大小，甚至是工作集，那么这就是买卖协议。

``````public double StandardDeviation(List<double> valueList, double ma)
{
double xMinusMovAvg = 0.0;
double Sigma = 0.0;
int k = valueList.Count;

foreach (double value in valueList){
xMinusMovAvg = value - ma;
Sigma = Sigma + (xMinusMovAvg * xMinusMovAvg);
}
return Math.Sqrt(Sigma / (k - 1));
}
``````

``````using System;
using System.Collections.Generic;

namespace SampleApp
{
internal class Program
{
private static void Main()
{
List<double> data = new List<double> {1, 2, 3, 4, 5, 6};

double mean = data.Mean();
double variance = data.Variance();
double sd = data.StandardDeviation();

Console.WriteLine("Mean: {0}, Variance: {1}, SD: {2}", mean, variance, sd);
Console.WriteLine("Press any key to continue...");
}
}

public static class MyListExtensions
{
public static double Mean(this List<double> values)
{
return values.Count == 0 ? 0 : values.Mean(0, values.Count);
}

public static double Mean(this List<double> values, int start, int end)
{
double s = 0;

for (int i = start; i < end; i++)
{
s += values[i];
}

return s / (end - start);
}

public static double Variance(this List<double> values)
{
return values.Variance(values.Mean(), 0, values.Count);
}

public static double Variance(this List<double> values, double mean)
{
return values.Variance(mean, 0, values.Count);
}

public static double Variance(this List<double> values, double mean, int start, int end)
{
double variance = 0;

for (int i = start; i < end; i++)
{
variance += Math.Pow((values[i] - mean), 2);
}

int n = end - start;
if (start > 0) n -= 1;

return variance / (n);
}

public static double StandardDeviation(this List<double> values)
{
return values.Count == 0 ? 0 : values.StandardDeviation(0, values.Count);
}

public static double StandardDeviation(this List<double> values, int start, int end)
{
double mean = values.Mean(start, end);
double variance = values.Variance(mean, start, end);

return Math.Sqrt(variance);
}
}
}
``````

``````/// <summary>
/// Calculates standard deviation, same as MATLAB std(X,0) function
/// <seealso cref="http://www.mathworks.co.uk/help/techdoc/ref/std.html"/>
/// </summary>
/// <param name="values">enumumerable data</param>
/// <returns>Standard deviation</returns>
public static double GetStandardDeviation(this IEnumerable<double> values)
{
//validation
if (values == null)
throw new ArgumentNullException();

int lenght = values.Count();

//saves from devision by 0
if (lenght == 0 || lenght == 1)
return 0;

double sum = 0.0, sum2 = 0.0;

for (int i = 0; i < lenght; i++)
{
double item = values.ElementAt(i);
sum += item;
sum2 += item * item;
}

return Math.Sqrt((sum2 - sum * sum / lenght) / (lenght - 1));
}
``````

``````private double calculateStdDev(List<double> values)
{
double average = values.Average();
return Math.Sqrt((values.Select(val => (val - average) * (val - average)).Sum()) / values.Count);
}
``````

``````public final class StatMeasure {
private StatMeasure() {}

public interface Stats1D {

/** Add a value to the population */

/** Get the mean of all the added values */
double getMean();

/** Get the standard deviation from a sample of the population. */
double getStDevSample();

/** Gets the standard deviation for the entire population. */
double getStDevPopulation();
}

private static class WaldorfPopulation implements Stats1D {
private double mean = 0.0;
private double sSum = 0.0;
private int count = 0;

@Override
double tmpMean = mean;
double delta = value - tmpMean;
mean += delta / ++count;
sSum += delta * (value - mean);
}

@Override
public double getMean() { return mean; }

@Override
public double getStDevSample() { return Math.sqrt(sSum / (count - 1)); }

@Override
public double getStDevPopulation() { return Math.sqrt(sSum / (count)); }
}

private static class StandardPopulation implements Stats1D {
private double sum = 0.0;
private double sumOfSquares = 0.0;
private int count = 0;

@Override
sum += value;
sumOfSquares += value * value;
count++;
}

@Override
public double getMean() { return sum / count; }

@Override
public double getStDevSample() {
return (float) Math.sqrt((sumOfSquares - ((sum * sum) / count)) / (count - 1));
}

@Override
public double getStDevPopulation() {
return (float) Math.sqrt((sumOfSquares - ((sum * sum) / count)) / count);
}
}

/**
* Returns a way to measure a population of data using Waldorf's method.
* This method is better if your population or values are so large that
* the sum of x-squared may overflow. It's also probably faster if you
* need to recalculate the mean and standard deviation continuously,
* for example, if you are continually updating a graphic of the data as
* it flows in.
*
* @return A Stats1D object that uses Waldorf's method.
*/
public static Stats1D getWaldorfStats() { return new WaldorfPopulation(); }

/**
* Return a way to measure the population of data using the sum-of-squares
* method. This is probably faster than Waldorf's method, but runs the
* risk of data overflow.
*
* @return A Stats1D object that uses the sum-of-squares method
*/
public static Stats1D getSumOfSquaresStats() { return new StandardPopulation(); }
}
``````