Perhaps this would work:

diff --git a/Lib/statistics.py b/Lib/statistics.py
index c76a6ca519..93a4633464 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -682,8 +682,10 @@ def _ss(data, c=None):
     calculated from ``c`` as given. Use the second case with care, as it can
     lead to garbage results.
     """
-    if c is None:
-        c = mean(data)
+    if c is not None:
+        T, total, count = _sum((x-c)**2 for x in data)
+        return (T, total)
+    c = mean(data)
     T, total, count = _sum((x-c)**2 for x in data)
     # The following sum should mathematically equal zero, but due to rounding
     # error may not.


Matti, where do you get 0.5 as the expected outcome for the third example?   The actual mean is 1.5, so I would expect the third case to give sqrt(2)/2 or 0.707.