样本方差与样本标准差
1、定义：样本中各数据与样本平均数的差的平方和的平均数叫做样本方差；样本方差的算术平方根叫做样本标准差。
注：样本方差和样本标准差都是衡量一个样本波动大小的量，样本方差或样本标准差越大，样本数据的波动就越大。
标准差与标准方差
1、定义：方差是各个数据与平均数之差的平方和的平均数。在概率论和数理统计中，方差用来度量随机变量和其数学期望（即均值）之间的偏离程度。标准差在概率统计中最常使用作为统计分布程度上的测量。标准差定义为方差的算术平方根，反映组内个体间的离散程度。
加权平均
1、定义：加权平均数（weighted average）是不同比重数据的平均数，就是把原始数据按照合理的比例来计算。
算法代码如下：
public static double StandardDeviation(this IListsource) { if (source == null) { throw new ArgumentNullException("source"); } if (source.Count == 0) { return double.NaN; } double variance = source.Variance(); return Math.Sqrt(variance); } public static double SampleStandardDeviation(this IList source) { if (source == null) { throw new ArgumentNullException("source"); } if (source.Count == 0 || source.Count == 1) { return double.NaN; } double variance = source.SampleVariance(); return Math.Sqrt(variance); } public static double Variance(this IList source) { if (source == null) { throw new ArgumentNullException("source"); } if (source.Count == 0) { return double.NaN; } int count = source.Count(); double deviation = CalculateDeviation(source, count); return deviation / count; } public static double SampleVariance(this IList source) { if (source == null) { throw new ArgumentNullException("source"); ; } if (source.Count == 0 || source.Count == 1) { return double.NaN; } int count = source.Count(); double deviation = CalculateDeviation(source, count); return deviation / (count - 1); } public static double WeightedAverage(this IList source, IList factors) { if (source == null) { throw new ArgumentNullException("source"); } if (source.Count != factors.Count) { throw new ArgumentException("source count is not equal to factors count."); } if (source.Count == 0) { return double.NaN; } double sum = factors.Sum(); if (sum == 0) { return double.NaN; } double weight = 0; for (int index = 0; index < factors.Count; index++) { weight += source[index] * (factors[index] / sum); } return weight; } private static double CalculateDeviation(IList source, int count) { double avg = source.Average(); double deviation = 0; for (int index = 0; index < count; index++) { deviation += (source[index] - avg) * (source[index] - avg); } return deviation; }
