diff --git a/array_api_strict/_statistical_functions.py b/array_api_strict/_statistical_functions.py
index 35876dda..023bb871 100644
--- a/array_api_strict/_statistical_functions.py
+++ b/array_api_strict/_statistical_functions.py
@@ -153,8 +153,8 @@ def std(
     keepdims: bool = False,
 ) -> Array:
     # Note: the keyword argument correction is different here
-    if x.dtype not in _real_floating_dtypes:
-        raise TypeError("Only real floating-point dtypes are allowed in std")
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in std")
     return Array._new(np.std(x._array, axis=axis, ddof=correction, keepdims=keepdims), device=x.device)
 
 
@@ -185,6 +185,6 @@ def var(
     keepdims: bool = False,
 ) -> Array:
     # Note: the keyword argument correction is different here
-    if x.dtype not in _real_floating_dtypes:
-        raise TypeError("Only real floating-point dtypes are allowed in var")
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in var")
     return Array._new(np.var(x._array, axis=axis, ddof=correction, keepdims=keepdims), device=x.device)