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 d659013e41..e4ffa5ee42 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -127,7 +127,79 @@ SELECT var_samp(b::numeric) FROM aggtest;
 
 -- population variance is defined for a single tuple, sample variance
 -- is not
-SELECT var_pop(1.0), var_samp(2.0);
+SELECT var_pop(1.0::float8), var_samp(2.0::float8);
+ var_pop | var_samp 
+---------+----------
+       0 |         
+(1 row)
+
+SELECT stddev_pop(3.0::float8), stddev_samp(4.0::float8);
+ stddev_pop | stddev_samp 
+------------+-------------
+          0 |            
+(1 row)
+
+SELECT var_pop('inf'::float8), var_samp('inf'::float8);
+ var_pop | var_samp 
+---------+----------
+     NaN |         
+(1 row)
+
+SELECT stddev_pop('inf'::float8), stddev_samp('inf'::float8);
+ stddev_pop | stddev_samp 
+------------+-------------
+        NaN |            
+(1 row)
+
+SELECT var_pop('nan'::float8), var_samp('nan'::float8);
+ var_pop | var_samp 
+---------+----------
+     NaN |         
+(1 row)
+
+SELECT stddev_pop('nan'::float8), stddev_samp('nan'::float8);
+ stddev_pop | stddev_samp 
+------------+-------------
+        NaN |            
+(1 row)
+
+SELECT var_pop(1.0::float4), var_samp(2.0::float4);
+ var_pop | var_samp 
+---------+----------
+       0 |         
+(1 row)
+
+SELECT stddev_pop(3.0::float4), stddev_samp(4.0::float4);
+ stddev_pop | stddev_samp 
+------------+-------------
+          0 |            
+(1 row)
+
+SELECT var_pop('inf'::float4), var_samp('inf'::float4);
+ var_pop | var_samp 
+---------+----------
+     NaN |         
+(1 row)
+
+SELECT stddev_pop('inf'::float4), stddev_samp('inf'::float4);
+ stddev_pop | stddev_samp 
+------------+-------------
+        NaN |            
+(1 row)
+
+SELECT var_pop('nan'::float4), var_samp('nan'::float4);
+ var_pop | var_samp 
+---------+----------
+     NaN |         
+(1 row)
+
+SELECT stddev_pop('nan'::float4), stddev_samp('nan'::float4);
+ stddev_pop | stddev_samp 
+------------+-------------
+        NaN |            
+(1 row)
+
+SELECT var_pop(1.0::numeric), var_samp(2.0::numeric);
  var_pop | var_samp 
 ---------+----------
        0 |         
@@ -139,6 +211,18 @@ SELECT stddev_pop(3.0::numeric), stddev_samp(4.0::numeric);
           0 |            
 (1 row)
 
+SELECT var_pop('nan'::numeric), var_samp('nan'::numeric);
+ var_pop | var_samp 
+---------+----------
+     NaN |      NaN
+(1 row)
+
+SELECT stddev_pop('nan'::numeric), stddev_samp('nan'::numeric);
+ stddev_pop | stddev_samp 
+------------+-------------
+        NaN |         NaN
+(1 row)
+
 -- verify correct results for null and NaN inputs
 select sum(null::int4) from generate_series(1,3);
  sum 
@@ -299,6 +383,25 @@ SELECT corr(b, a) FROM aggtest;
  0.139634516517873
 (1 row)
 
+-- check single-tuple behavior
+SELECT covar_pop(1::float8,2::float8), covar_samp(3::float8,4::float8);
+ covar_pop | covar_samp 
+-----------+------------
+         0 |           
+(1 row)
+
+SELECT covar_pop(1::float8,'inf'::float8), covar_samp(3::float8,'inf'::float8);
+ covar_pop | covar_samp 
+-----------+------------
+       NaN |           
+(1 row)
+
+SELECT covar_pop(1::float8,'nan'::float8), covar_samp(3::float8,'nan'::float8);
+ covar_pop | covar_samp 
+-----------+------------
+       NaN |           
+(1 row)
+
 -- test accum and combine functions directly
 CREATE TABLE regr_test (x float8, y float8);
 INSERT INTO regr_test VALUES (10,150),(20,250),(30,350),(80,540),(100,200);
diff --git a/src/test/regress/sql/aggregates.sql b/src/test/regress/sql/aggregates.sql
index 2a066f5a3a..044d515507 100644
--- a/src/test/regress/sql/aggregates.sql
+++ b/src/test/regress/sql/aggregates.sql
@@ -39,8 +39,22 @@ SELECT var_samp(b::numeric) FROM aggtest;
 
 -- population variance is defined for a single tuple, sample variance
 -- is not
-SELECT var_pop(1.0), var_samp(2.0);
+SELECT var_pop(1.0::float8), var_samp(2.0::float8);
+SELECT stddev_pop(3.0::float8), stddev_samp(4.0::float8);
+SELECT var_pop('inf'::float8), var_samp('inf'::float8);
+SELECT stddev_pop('inf'::float8), stddev_samp('inf'::float8);
+SELECT var_pop('nan'::float8), var_samp('nan'::float8);
+SELECT stddev_pop('nan'::float8), stddev_samp('nan'::float8);
+SELECT var_pop(1.0::float4), var_samp(2.0::float4);
+SELECT stddev_pop(3.0::float4), stddev_samp(4.0::float4);
+SELECT var_pop('inf'::float4), var_samp('inf'::float4);
+SELECT stddev_pop('inf'::float4), stddev_samp('inf'::float4);
+SELECT var_pop('nan'::float4), var_samp('nan'::float4);
+SELECT stddev_pop('nan'::float4), stddev_samp('nan'::float4);
+SELECT var_pop(1.0::numeric), var_samp(2.0::numeric);
 SELECT stddev_pop(3.0::numeric), stddev_samp(4.0::numeric);
+SELECT var_pop('nan'::numeric), var_samp('nan'::numeric);
+SELECT stddev_pop('nan'::numeric), stddev_samp('nan'::numeric);
 
 -- verify correct results for null and NaN inputs
 select sum(null::int4) from generate_series(1,3);
@@ -81,6 +95,11 @@ SELECT regr_slope(b, a), regr_intercept(b, a) FROM aggtest;
 SELECT covar_pop(b, a), covar_samp(b, a) FROM aggtest;
 SELECT corr(b, a) FROM aggtest;
 
+-- check single-tuple behavior
+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);
+SELECT covar_pop(1::float8,'nan'::float8), covar_samp(3::float8,'nan'::float8);
+
 -- test accum and combine functions directly
 CREATE TABLE regr_test (x float8, y float8);
 INSERT INTO regr_test VALUES (10,150),(20,250),(30,350),(80,540),(100,200);