Just a short one again. This time I will explain the **coefficient of variation**. And once again give you a full code example of how you can implement it in c#.

The coefficient of variation (CV) is a normalized measure of dispersion. It is a measure of consistency indicating the uniformity in the values of the signal from the mean of the signal. A smaller coefficient of variation indicates a more consistent signal. The values are more uniformly dispersed.

Coefficient of variation is useful when comparing data with different units. For example in the SoapSynergy project I am working on I often have to make comparisons between displacement and angles. Since those signals have different units ((centi)meters versus degrees) it is useful to have a dimensionless number to compare with.

The downside of the coefficient of variation is that it is quite sensitive to changes in the mean. So if your signal moves around the 0 (as a sine wave does) making your mean ~=0, the coefficient of variation can quickly jump to near infinite numbers rendering it useless. For this reason I chose to calculate the coefficient of variation using the absolute values of my signals.

using System; using System.Collections.Generic; namespace SampleApp { internal static class Program { private const float CompareIsZeroTolerance = 0.000000000001f; private static void Main() { List<double> data = new List<double> {1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2}; double mean = data.Mean(); double sd = data.StandardDeviation(); double cv = CoefficientOfVariance(sd, mean); Console.WriteLine("CV: {0}, (mean: {1}, sd: {2})", cv, mean, sd); Console.WriteLine("Press any key to continue..."); Console.ReadKey(); } private static double CoefficientOfVariance(double sd, double mean) { if (Math.Abs(mean - 0) < CompareIsZeroTolerance) return 0; return sd / mean; } } public static class MyListExtensions { public static double Mean(this List<double> values) { return values.Count == 0 ? 0 : values.Mean(0, values.Count); } private static double Mean(this IList<double> values, int start, int end) { double s = 0; for (int i = start; i < end; i++) { s += values[i]; } return s / (end - start); } private static double Variance(this IList<double> values, double mean, int start, int end) { double variance = 0; int i; for (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); } private static double StandardDeviation(this IList<double> values, int start, int end) { double mean = values.Mean(start, end); double variance = values.Variance(mean, start, end); return Math.Sqrt(variance); } } }