diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 2101d58674..6a717f19bb 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -2925,6 +2925,17 @@ float8_accum(PG_FUNCTION_ARGS)
 			Sxx = get_float8_nan();
 		}
 	}
+	else
+	{
+		/*
+		 * At the first input, we normally can leave Sxx as 0.  However, if
+		 * the first input is Inf or NaN, we'd better force Sxx to NaN;
+		 * otherwise we will falsely report variance zero when there are no
+		 * more inputs.
+		 */
+		if (isnan(newval) || isinf(newval))
+			Sxx = get_float8_nan();
+	}
 
 	/*
 	 * If we're invoked as an aggregate, we can cheat and modify our first
@@ -2999,6 +3010,17 @@ float4_accum(PG_FUNCTION_ARGS)
 			Sxx = get_float8_nan();
 		}
 	}
+	else
+	{
+		/*
+		 * At the first input, we normally can leave Sxx as 0.  However, if
+		 * the first input is Inf or NaN, we'd better force Sxx to NaN;
+		 * otherwise we will falsely report variance zero when there are no
+		 * more inputs.
+		 */
+		if (isnan(newval) || isinf(newval))
+			Sxx = get_float8_nan();
+	}
 
 	/*
 	 * If we're invoked as an aggregate, we can cheat and modify our first
@@ -3225,6 +3247,19 @@ float8_regr_accum(PG_FUNCTION_ARGS)
 				Sxy = get_float8_nan();
 		}
 	}
+	else
+	{
+		/*
+		 * At the first input, we normally can leave Sxx et al as 0.  However,
+		 * if the first input is Inf or NaN, we'd better force the dependent
+		 * sums to NaN; otherwise we will falsely report variance zero when
+		 * there are no more inputs.
+		 */
+		if (isnan(newvalX) || isinf(newvalX))
+			Sxx = Sxy = get_float8_nan();
+		if (isnan(newvalY) || isinf(newvalY))
+			Syy = Sxy = get_float8_nan();
+	}
 
 	/*
 	 * If we're invoked as an aggregate, we can cheat and modify our first
diff --git a/src/test/regress/expected/aggregates.out b/src/test/regress/expected/aggregates.out
index 0a6884d382..e4ffa5ee42 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -142,25 +142,25 @@ SELECT stddev_pop(3.0::float8), stddev_samp(4.0::float8);
 SELECT var_pop('inf'::float8), var_samp('inf'::float8);
  var_pop | var_samp 
 ---------+----------
-       0 |         
+     NaN |         
 (1 row)
 
 SELECT stddev_pop('inf'::float8), stddev_samp('inf'::float8);
  stddev_pop | stddev_samp 
 ------------+-------------
-          0 |            
+        NaN |            
 (1 row)
 
 SELECT var_pop('nan'::float8), var_samp('nan'::float8);
  var_pop | var_samp 
 ---------+----------
-       0 |         
+     NaN |         
 (1 row)
 
 SELECT stddev_pop('nan'::float8), stddev_samp('nan'::float8);
  stddev_pop | stddev_samp 
 ------------+-------------
-          0 |            
+        NaN |            
 (1 row)
 
 SELECT var_pop(1.0::float4), var_samp(2.0::float4);
@@ -178,25 +178,25 @@ SELECT stddev_pop(3.0::float4), stddev_samp(4.0::float4);
 SELECT var_pop('inf'::float4), var_samp('inf'::float4);
  var_pop | var_samp 
 ---------+----------
-       0 |         
+     NaN |         
 (1 row)
 
 SELECT stddev_pop('inf'::float4), stddev_samp('inf'::float4);
  stddev_pop | stddev_samp 
 ------------+-------------
-          0 |            
+        NaN |            
 (1 row)
 
 SELECT var_pop('nan'::float4), var_samp('nan'::float4);
  var_pop | var_samp 
 ---------+----------
-       0 |         
+     NaN |         
 (1 row)
 
 SELECT stddev_pop('nan'::float4), stddev_samp('nan'::float4);
  stddev_pop | stddev_samp 
 ------------+-------------
-          0 |            
+        NaN |            
 (1 row)
 
 SELECT var_pop(1.0::numeric), var_samp(2.0::numeric);
@@ -393,13 +393,13 @@ SELECT covar_pop(1::float8,2::float8), covar_samp(3::float8,4::float8);
 SELECT covar_pop(1::float8,'inf'::float8), covar_samp(3::float8,'inf'::float8);
  covar_pop | covar_samp 
 -----------+------------
-         0 |           
+       NaN |           
 (1 row)
 
 SELECT covar_pop(1::float8,'nan'::float8), covar_samp(3::float8,'nan'::float8);
  covar_pop | covar_samp 
 -----------+------------
-         0 |           
+       NaN |           
 (1 row)
 
 -- test accum and combine functions directly