diff --git a/src/Numerics/Statistics/Statistics.cs b/src/Numerics/Statistics/Statistics.cs
index dd2d3baf..9a957609 100644
--- a/src/Numerics/Statistics/Statistics.cs
+++ b/src/Numerics/Statistics/Statistics.cs
@@ -88,7 +88,7 @@ namespace MathNet.Numerics.Statistics
         }
 
         /// <summary>
-        /// Calculates the unbiased population variance estimator (on a dataset of size N will use an N-1 normalizer).
+        /// Calculates the unbiased population (sample) variance estimator (on a dataset of size N will use an N-1 normalizer).
         /// </summary>
         /// <param name="data">The data to calculate the variance of.</param>
         /// <returns>The unbiased population variance of the sample.</returns>
@@ -121,11 +121,11 @@ namespace MathNet.Numerics.Statistics
                 }
             }
 
-            return variance / (j - 1);
+            return j > 1 ? variance/(j - 1) : double.NaN;
         }
 
         /// <summary>
-        /// Computes the unbiased population variance estimator (on a dataset of size N will use an N-1 normalizer) for nullable data.
+        /// Computes the unbiased population (sample) variance estimator (on a dataset of size N will use an N-1 normalizer) for nullable data.
         /// </summary>
         /// <param name="data">The data to calculate the variance of.</param>
         /// <returns>The population variance of the sample.</returns>
@@ -171,7 +171,7 @@ namespace MathNet.Numerics.Statistics
                 }
             }
 
-            return variance / (j - 1);
+            return j > 1 ? variance/(j - 1) : double.NaN;
         }
 
         /// <summary>
diff --git a/src/UnitTests/StatisticsTests/StatisticsTests.cs b/src/UnitTests/StatisticsTests/StatisticsTests.cs
index 1b6f51cf..a7bb8170 100644
--- a/src/UnitTests/StatisticsTests/StatisticsTests.cs
+++ b/src/UnitTests/StatisticsTests/StatisticsTests.cs
@@ -227,6 +227,22 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
             AssertHelpers.AlmostEqual(2d, Statistics.StandardDeviation(gaussian.Samples().Take(10000)), 2);
         }
 
+        [Test]
+        public void SampleVarianceOfEmptyAndSingleMustBeNaN()
+        {
+            Assert.That(Statistics.Variance(new double[0]), Is.NaN);
+            Assert.That(Statistics.Variance(new[] { 2d }), Is.NaN);
+            Assert.That(Statistics.Variance(new[] { 2d, 3d }), Is.Not.NaN);
+        }
+
+        [Test]
+        public void PopulationVarianceOfEmptyMustBeNaN()
+        {
+            Assert.That(Statistics.PopulationVariance(new double[0]), Is.NaN);
+            Assert.That(Statistics.PopulationVariance(new[] { 2d }), Is.Not.NaN);
+            Assert.That(Statistics.PopulationVariance(new[] { 2d, 3d }), Is.Not.NaN);
+        }
+
         /// <summary>
         /// URL http://mathnetnumerics.codeplex.com/workitem/5667
         /// </summary>