diff --git a/docs/CHANGELOG.md b/docs/CHANGELOG.md
index a1ce1bc9..e0291e1b 100644
--- a/docs/CHANGELOG.md
+++ b/docs/CHANGELOG.md
@@ -1,5 +1,11 @@
 # What's new in boost-histogram
 
+## UPCOMING
+
+* Support running type checking from Python < 3.8 [#542][]
+
+[#542]: https://github.com/scikit-hep/boost-histogram/pull/542
+
 ## Version 1.0
 
 ### Version 1.0.1
diff --git a/src/boost_histogram/_core/accumulators.pyi b/src/boost_histogram/_core/accumulators.pyi
index cf38d65c..3cd00af2 100644
--- a/src/boost_histogram/_core/accumulators.pyi
+++ b/src/boost_histogram/_core/accumulators.pyi
@@ -19,7 +19,7 @@ class WeightedSum(_BaseAccumulator):
     def value(self) -> float: ...
     @property
     def variance(self) -> float: ...
-    def __iadd__(self: T, val: float, /) -> T: ...
+    def __iadd__(self: T, arg0: float) -> T: ...
     def fill(self: T, value: ArrayLike, variance: ArrayLike | None = None) -> T: ...
     @staticmethod
     def _make(self: T, a: ArrayLike, b: ArrayLike) -> T: ...
@@ -32,7 +32,7 @@ class Sum(_BaseAccumulator):
     def __init__(self, value: float | None) -> None: ...
     @property
     def value(self) -> float: ...
-    def __iadd__(self: T, val: float, /) -> T: ...
+    def __iadd__(self: T, arg0: float) -> T: ...
     def fill(self: T, value: ArrayLike) -> T: ...
     @property
     def _small(self) -> float: ...
@@ -63,11 +63,11 @@ class WeightedMean(_BaseAccumulator):
     def fill(self: T, value: ArrayLike, *, weight: ArrayLike | None = None) -> T: ...
     @staticmethod
     def _make(
-        self: T, a: ArrayLike, b: ArrayLike, c: ArrayLike, d: ArrayLike, /
+        self: T, arg0: ArrayLike, arg1: ArrayLike, arg2: ArrayLike, arg3: ArrayLike
     ) -> T: ...
     @staticmethod
     def _array(
-        self: T, a: ArrayLike, b: ArrayLike, c: ArrayLike, d: ArrayLike, /
+        self: T, arg0: ArrayLike, arg1: ArrayLike, arg2: ArrayLike, arg3: ArrayLike
     ) -> T: ...
     def __getitem__(self, key: str) -> float: ...
     def __setitem__(self, key: str, value: float) -> None: ...
@@ -87,12 +87,8 @@ class Mean(_BaseAccumulator):
     ) -> T: ...
     def fill(self: T, value: ArrayLike, *, weight: ArrayLike | None = None) -> T: ...
     @staticmethod
-    def _make(
-        self: T, a: ArrayLike, b: ArrayLike, c: ArrayLike, d: ArrayLike, /
-    ) -> T: ...
+    def _make(self: T, arg0: ArrayLike, arg1: ArrayLike, arg2: ArrayLike) -> T: ...
     @staticmethod
-    def _array(
-        self: T, a: ArrayLike, b: ArrayLike, c: ArrayLike, d: ArrayLike, /
-    ) -> T: ...
+    def _array(self: T, arg0: ArrayLike, arg1: ArrayLike, arg2: ArrayLike) -> T: ...
     def __getitem__(self, key: str) -> float: ...
     def __setitem__(self, key: str, value: float) -> None: ...
diff --git a/tests/test_accumulators.py b/tests/test_accumulators.py
index fc7c0da5..4eb9b21b 100644
--- a/tests/test_accumulators.py
+++ b/tests/test_accumulators.py
@@ -94,7 +94,7 @@ def test_mean():
 
 
 float_st = st.floats(
-    allow_nan=False, allow_infinity=False, min_value=-1e5, max_value=1e5
+    allow_nan=False, allow_infinity=False, min_value=-1e4, max_value=1e4
 )
 simple_list_st = st.lists(float_st, min_size=1, max_size=10)
 
@@ -129,7 +129,7 @@ def test_sum_mean(list1, list2):
         st.lists(float_st, min_size=n, max_size=n),
         st.lists(
             st.floats(
-                allow_nan=False, allow_infinity=False, min_value=1e-2, max_value=1e3
+                allow_nan=False, allow_infinity=False, min_value=1e-2, max_value=1e2
             ),
             min_size=n,
             max_size=n,
@@ -151,12 +151,12 @@ def test_sum_weighed_mean(pair1, pair2):
 
     ab = a + b
     assert ab.value == approx(c.value)
-    assert ab.variance == approx(c.variance, nan_ok=True, abs=1e-7, rel=1e-3)
+    assert ab.variance == approx(c.variance, nan_ok=True, abs=1e-3, rel=1e-2)
     assert ab.sum_of_weights == approx(c.sum_of_weights)
     assert ab.sum_of_weights_squared == approx(c.sum_of_weights_squared)
 
     a += b
     assert a.value == approx(c.value)
-    assert a.variance == approx(c.variance, nan_ok=True, abs=1e-7, rel=1e-3)
+    assert a.variance == approx(c.variance, nan_ok=True, abs=1e-3, rel=1e-2)
     assert a.sum_of_weights == approx(c.sum_of_weights)
     assert a.sum_of_weights_squared == approx(c.sum_of_weights_squared)