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+#pragma once
+
+#include <cmath>
+
+// no copyright information other than the attribution below.
+
+// code shared as an example/tutorial of running variance
+// written by John D. Cook on the website <http://www.johndcook.com/blog/standard_deviation>
+
+// following references in the site's article:
+
+// Chan, Tony F.; Golub, Gene H.; LeVeque, Randall J. (1983).
+// Algorithms for Computing the Sample Variance: Analysis and Recommendations.
+// The American Statistician 37, 242-247.
+
+// Ling, Robert F. (1974).
+// Comparison of Several Algorithms for Computing Sample Means and Variances.
+// Journal of the American Statistical Association, Vol. 69, No. 348, 859-866.
+
+struct variance final
+{
+    using size_type = unsigned;
+
+    variance& operator=(variance const&) = default;
+    void clear() { *this = {}; }
+
+    constexpr size_type count() const { return cnt; }
+
+    constexpr double avg() const { return cnt > 0 ? m_new : 0; }
+    constexpr double Var() const { return cnt > 1 ? s_new/(cnt - 1) : 0; }
+    double stddev() const { return std::sqrt(Var()); }
+
+    void input(double x)
+    {
+        cnt++;
+
+        if (cnt == 1)
+        {
+            m_old = m_new = x;
+            s_old = 0;
+        }
+        else
+        {
+            m_new = m_old + (x - m_old)/cnt;
+            s_new = s_old + (x - m_old)*(x - m_new);
+
+            m_old = m_new;
+            s_old = s_new;
+        }
+    }
+
+private:
+    double m_old, m_new, s_old, s_new;
+    size_type cnt = 0;
+};