算法--样本方差、样本标准差、方差、标准方差与加权平均

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 IList<double> source)        {            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<double> 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<double> 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<double> 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<double> source, IList<double> 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<double> 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;        }