diff --git a/mysql-test/r/func_group.result b/mysql-test/r/func_group.result
index 5192251795b..57b109e1ee6 100644
--- a/mysql-test/r/func_group.result
+++ b/mysql-test/r/func_group.result
@@ -648,3 +648,11 @@ select a from t1 having a=1;
 a
 1
 drop table t1;
+create table t1 (a int);
+select variance(2) from t1;
+variance(2)
+NULL
+select stddev(2) from t1;
+stddev(2)
+NULL
+drop table t1;
diff --git a/mysql-test/t/func_group.test b/mysql-test/t/func_group.test
index a1acf5f89eb..7966a2262f4 100644
--- a/mysql-test/t/func_group.test
+++ b/mysql-test/t/func_group.test
@@ -387,3 +387,12 @@ insert into t1 values (1);
 select max(a) as b from t1 having b=1;
 select a from t1 having a=1;
 drop table t1;
+
+#
+# Bug #3435: variance(const), stddev(const) and an empty table
+#
+
+create table t1 (a int);
+select variance(2) from t1;
+select stddev(2) from t1;
+drop table t1;
diff --git a/sql/item_sum.h b/sql/item_sum.h
index 9593c8ddbba..d7753303f55 100644
--- a/sql/item_sum.h
+++ b/sql/item_sum.h
@@ -351,6 +351,7 @@ class Item_sum_variance : public Item_sum_num
   void update_field();
   Item *result_item(Field *field)
   { return new Item_variance_field(this); }
+  void no_rows_in_result() {}
   const char *func_name() const { return "variance"; }
   Item *copy_or_same(THD* thd);
 };