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Add Welford's Variance (TheAlgorithms#358)
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‎Algorithms.Tests/Other/WelfordsVarianceTest.cs

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using Algorithms.Other;
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using NUnit.Framework;
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namespace Algorithms.Tests.Other
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{
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public class WelfordsVarianceTest
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{
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[Test]
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public void WelfordVariance_Example1()
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{
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var welfordsVariance = new WelfordsVariance();
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welfordsVariance.AddValue(4);
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welfordsVariance.AddValue(7);
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welfordsVariance.AddValue(13);
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welfordsVariance.AddValue(16);
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Assert.AreEqual(4, welfordsVariance.Count);
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Assert.AreEqual(10, welfordsVariance.Mean, 0.0000001);
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Assert.AreEqual(22.5, welfordsVariance.Variance, 0.0000001);
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Assert.AreEqual(30, welfordsVariance.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_Example2()
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{
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var stats = new WelfordsVariance();
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stats.AddValue(100000004);
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stats.AddValue(100000007);
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stats.AddValue(100000013);
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stats.AddValue(100000016);
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Assert.AreEqual(4, stats.Count);
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Assert.AreEqual(100000010, stats.Mean, 0.0000001);
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Assert.AreEqual(22.5, stats.Variance, 0.0000001);
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Assert.AreEqual(30, stats.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_Example3()
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{
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var stats = new WelfordsVariance();
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stats.AddValue(1000000004);
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stats.AddValue(1000000007);
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stats.AddValue(1000000013);
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stats.AddValue(1000000016);
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Assert.AreEqual(4, stats.Count);
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Assert.AreEqual(1000000010, stats.Mean, 0.0000001);
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Assert.AreEqual(22.5, stats.Variance, 0.0000001);
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Assert.AreEqual(30, stats.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_Example4()
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{
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var stats = new WelfordsVariance();
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stats.AddValue(6);
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stats.AddValue(2);
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stats.AddValue(3);
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stats.AddValue(1);
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Assert.AreEqual(4, stats.Count);
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Assert.AreEqual(3, stats.Mean, 0.0000001);
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Assert.AreEqual(3.5, stats.Variance, 0.0000001);
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Assert.AreEqual(4.6666667, stats.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_Example5()
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{
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var stats = new WelfordsVariance(new double[] { 2, 2, 5, 7 });
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Assert.AreEqual(4, stats.Count);
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Assert.AreEqual(4, stats.Mean, 0.0000001);
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Assert.AreEqual(4.5, stats.Variance, 0.0000001);
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Assert.AreEqual(6, stats.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_Example6()
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{
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var stats = new WelfordsVariance();
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stats.AddRange(new double[] { 2, 4, 4, 4, 5, 5, 7, 9 });
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Assert.AreEqual(8, stats.Count);
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Assert.AreEqual(5, stats.Mean, 0.0000001);
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Assert.AreEqual(4, stats.Variance, 0.0000001);
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Assert.AreEqual(4.5714286, stats.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_Example7()
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{
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var stats = new WelfordsVariance();
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stats.AddRange(new double[] { 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4 });
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Assert.AreEqual(20, stats.Count);
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Assert.AreEqual(7, stats.Mean, 0.0000001);
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Assert.AreEqual(8.9, stats.Variance, 0.0000001);
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Assert.AreEqual(9.3684211, stats.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_Example8()
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{
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var stats = new WelfordsVariance();
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stats.AddRange(new [] { 51.3, 55.6, 49.9, 52.0 });
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Assert.AreEqual(4, stats.Count);
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Assert.AreEqual(52.2, stats.Mean, 0.0000001);
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Assert.AreEqual(4.4250000, stats.Variance, 0.0000001);
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Assert.AreEqual(5.9000000, stats.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_Example9()
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{
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var stats = new WelfordsVariance();
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stats.AddRange(new double[] { -5, -3, -1, 1, 3 });
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Assert.AreEqual(5, stats.Count);
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Assert.AreEqual(-1, stats.Mean, 0.0000001);
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Assert.AreEqual(8, stats.Variance, 0.0000001);
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Assert.AreEqual(10, stats.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_Example10()
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{
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var stats = new WelfordsVariance();
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stats.AddRange(new double[] { -1, 0, 1 });
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Assert.AreEqual(3, stats.Count);
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Assert.AreEqual(0, stats.Mean, 0.0000001);
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Assert.AreEqual(0.6666667, stats.Variance, 0.0000001);
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Assert.AreEqual(1, stats.SampleVariance, 0.0000001);
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}
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[Test]
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public void WelfordVariance_NoValue()
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{
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var stats = new WelfordsVariance();
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Assert.AreEqual(0, stats.Count);
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Assert.AreEqual(double.NaN, stats.Mean);
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Assert.AreEqual(double.NaN, stats.Variance);
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Assert.AreEqual(double.NaN, stats.SampleVariance);
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}
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[Test]
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public void WelfordVariance_OneValue()
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{
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var stats = new WelfordsVariance();
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stats.AddValue(1);
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Assert.AreEqual(1, stats.Count);
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Assert.AreEqual(double.NaN, stats.Mean);
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Assert.AreEqual(double.NaN, stats.Variance);
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Assert.AreEqual(double.NaN, stats.SampleVariance);
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}
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[Test]
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public void WelfordVariance_TwoValues()
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{
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var stats = new WelfordsVariance();
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stats.AddValue(1);
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stats.AddValue(2);
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Assert.AreEqual(2, stats.Count);
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Assert.AreEqual(1.5, stats.Mean, 0.0000001);
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Assert.AreEqual(0.25, stats.Variance, 0.0000001);
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Assert.AreEqual(0.5, stats.SampleVariance, 0.0000001);
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}
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}
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}

‎Algorithms/Other/WelfordsVariance.cs

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using System;
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using System.Collections.Generic;
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using System.Linq;
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using System.Text;
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using System.Threading.Tasks;
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namespace Algorithms.Other
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{
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/// <summary>Implementation of Welford's variance algorithm.
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/// </summary>
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public class WelfordsVariance
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{
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/// <summary>
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/// Mean accumulates the mean of the entire dataset,
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/// m2 aggregates the squared distance from the mean,
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/// count aggregates the number of samples seen so far.
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/// </summary>
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private int count;
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public double Count => count;
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private double mean;
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public double Mean => count > 1 ? mean : double.NaN;
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private double m2;
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public double Variance => count > 1 ? m2 / count : double.NaN;
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public double SampleVariance => count > 1 ? m2 / (count - 1) : double.NaN;
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public WelfordsVariance()
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{
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count = 0;
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mean = 0;
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}
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public WelfordsVariance(double[] values)
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{
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count = 0;
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mean = 0;
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AddRange(values);
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}
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public void AddValue(double newValue)
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{
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count++;
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AddValueToDataset(newValue);
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}
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public void AddRange(double[] values)
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{
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var length = values.Length;
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for (var i = 1; i <= length; i++)
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{
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count++;
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AddValueToDataset(values[i - 1]);
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}
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}
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private void AddValueToDataset(double newValue)
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{
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var delta1 = newValue - mean;
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var newMean = mean + delta1 / count;
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var delta2 = newValue - newMean;
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m2 += delta1 * delta2;
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mean = newMean;
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}
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}
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}

‎README.md

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@@ -184,6 +184,7 @@ find more than one implementation for the same objective but using different alg
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* [Pareto Optimization](./Algorithms/Other/ParetoOptimization.cs)
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* [Gauss Optimization](./Algorithms/Other/GaussOptimization.cs)
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* [Decisions Convolutions](./Algorithms/Other/DecisionsConvolutions.cs)
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* [Welford's Variance](./Algorithms/Other/WelfordsVariance.cs)
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* [Problems](./Algorithms/Problems)
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* [Stable Marriage](./Algorithms/Problems/StableMarriage)
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* [Gale-Shapley](./Algorithms/Problems/StableMarriage/GaleShapley.cs)

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