The variation calculated in normal boost is not an unbiased variance but a sample variance. See: http://mathworld.wolfram.com/Variance.html This change makes boost to calculate unbiased variances normally.

boost-accumulators.diff

diff -ur /opt/local/include/boost/accumulators/statistics/covariance.hpp ../boost/accumulators/statistics/covariance.hpp
--- /opt/local/include/boost/accumulators/statistics/covariance.hpp             2013-05-31 08:41:19.000000000 +0900
+++ ../boost/accumulators/statistics/covariance.hpp	2013-06-05 19:09:33.000000000 +0900
@@ -141,7 +141,7 @@
         template<typename Args>
         void operator ()(Args const &args)
         {
-            std::size_t cnt = count(args);
+            cnt = count(args);
 
             if (cnt > 1)
             {
@@ -157,11 +157,12 @@
 
         result_type result(dont_care) const
         {
-            return this->cov_;
+            return numeric::average(this->cov_ * cnt, cnt - 1.);
         }
 
     private:
         result_type cov_;
+        std::size_t cnt;
     };
 
 } // namespace impl
diff -ur /opt/local/include/boost/accumulators/statistics/variance.hpp ../boost/accumulators/statistics/variance.hpp
--- /opt/local/include/boost/accumulators/statistics/variance.hpp	2013-05-31 08:41:19.000000000 +0900
+++ ../boost/accumulators/statistics/variance.hpp	2013-06-05 19:11:04.000000000 +0900
@@ -96,7 +96,7 @@
         template<typename Args>
         void operator ()(Args const &args)
         {
-            std::size_t cnt = count(args);
+            cnt = count(args);
 
             if(cnt > 1)
             {
@@ -110,11 +110,12 @@
 
         result_type result(dont_care) const
         {
-            return this->variance;
+            return numeric::average(this->variance * cnt, cnt - 1);
         }
 
     private:
         result_type variance;
+        std::size_t cnt;
     };
 
 } // namespace impl