参考链接：

https://www.johndcook.com/blog/standard_deviation/

https://www.zhihu.com/question/314505455/answer/1025527665

两种计算方差的公式

第一种：

第二种 ：

均值的计算方法

在线计算

 

附上代码：

class RunningStat { public: RunningStat() : m_n(0) {} void Clear() { m_n = 0; } void Push(double x) { m_n++; // See Knuth TAOCP vol 2, 3rd edition, page 232 if (m_n == 1) { m_oldM = m_newM = x; m_oldS = 0.0; } else { m_newM = m_oldM + (x - m_oldM)/m_n; m_newS = m_oldS + (x - m_oldM)*(x - m_newM); // set up for next iteration m_oldM = m_newM; m_oldS = m_newS; } } int NumDataValues() const { return m_n; } double Mean() const { return (m_n > 0) ? m_newM : 0.0; } double Variance() const { return ( (m_n > 1) ? m_newS/(m_n - 1) : 0.0 ); } double StandardDeviation() const { return sqrt( Variance() ); } private: int m_n; double m_oldM, m_newM, m_oldS, m_newS; }; 作者：星晴 链接：https://www.zhihu.com/question/314505455/answer/1025527665 来源：知乎 著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。 class RunningStats: def __init__(self): self.n = 0 self.old_m = 0 self.new_m = 0 self.old_s = 0 self.new_s = 0 def clear(self): self.n = 0 def push(self, x): self.n += 1 if self.n == 1: self.old_m = self.new_m = x self.old_s = 0 else: self.new_m = self.old_m + (x - self.old_m) / self.n self.new_s = self.old_s + (x - self.old_m) * (x - self.new_m) self.old_m = self.new_m self.old_s = self.new_s def mean(self): return self.new_m if self.n else 0.0 def variance(self): return self.new_s / (self.n - 1) if self.n > 1 else 0.0