diff --git a/heat/core/statistics.py b/heat/core/statistics.py
index 7608da7387..d6c0305a34 100644
--- a/heat/core/statistics.py
+++ b/heat/core/statistics.py
@@ -206,14 +206,12 @@ def average(
         Axis or axes along which to average ``x``.  The default,
         ``axis=None``, will average over all of the elements of the input array.
         If axis is negative it counts from the last to the first axis.
-        #TODO Issue #351: If axis is a tuple of ints, averaging is performed on all of the axes
-        specified in the tuple instead of a single axis or all the axes as
-        before.
     weights : DNDarray, optional
         An array of weights associated with the values in ``x``. Each value in
         ``x`` contributes to the average according to its associated weight.
         The weights array can either be 1D (in which case its length must be
         the size of ``x`` along the given axis) or of the same shape as ``x``.
+        Weighted average over tuple axis requires weights array to be of the same shape as ``x``.
         If ``weights=None``, then all data in ``x`` are assumed to have a
         weight equal to one, the result is equivalent to :func:`mean`.
     returned : bool, optional
@@ -269,7 +267,9 @@ def average(
             if axis is None:
                 raise TypeError("Axis must be specified when shapes of x and weights differ.")
             elif isinstance(axis, tuple):
-                raise NotImplementedError("Weighted average over tuple axis not implemented yet.")
+                raise ValueError(
+                    "Weighted average over tuple axis requires weights to be of the same shape as x."
+                )
             if weights.ndim != 1:
                 raise TypeError("1D weights expected when shapes of x and weights differ.")
             if weights.gshape[0] != x.gshape[axis]:
diff --git a/heat/core/tests/test_statistics.py b/heat/core/tests/test_statistics.py
index 922fd74aa8..2ce40a8201 100644
--- a/heat/core/tests/test_statistics.py
+++ b/heat/core/tests/test_statistics.py
@@ -306,7 +306,7 @@ def test_average(self):
             ht.average(random_5d, weights=random_weights.numpy(), axis=axis)
         with self.assertRaises(TypeError):
             ht.average(random_5d, weights=random_weights, axis=None)
-        with self.assertRaises(NotImplementedError):
+        with self.assertRaises(ValueError):
             ht.average(random_5d, weights=random_weights, axis=(1, 2))
         random_weights = ht.random.randn(random_5d.gshape[axis], random_5d.gshape[axis + 1])
         with self.assertRaises(TypeError):