BUG: Fix np.inf + np.nan sum issue on groupby mean

pandas/_libs/groupby.pyx

@@ -1075,6 +1075,13 @@ def group_mean(
                     y = val - compensation[lab, j]
                     t = sumx[lab, j] + y
                     compensation[lab, j] = t - sumx[lab, j] - y
+                    if compensation[lab, j] != compensation[lab, j]:
+                        # GH#50367
+                        # if val is +/- infinity, this (t-sumx[lab, j]-y) expression
+                        # will evaluate to Nan. So we are checking whether
+                        # compensation[lab, j] is Nan and setting it to 0.
+                        # we cannot use util.is_nan because of no gil
+                        compensation[lab, j] = 0.
                     sumx[lab, j] = t
 
         for i in range(ncounts):

pandas/tests/groupby/test_libgroupby.py

@@ -282,3 +282,23 @@ def test_cython_group_mean_not_datetimelike_but_has_NaT_values():
     tm.assert_numpy_array_equal(
         actual[:, 0], np.array(np.divide(np.add(data[0], data[1]), 2), dtype="float64")
     )
+
+
+def test_cython_group_mean_Inf_at_begining_and_end():
+    # GH 50367
+    actual = np.array([[np.nan, np.nan], [np.nan, np.nan]], dtype="float64")
+    counts = np.array([0, 0], dtype="int64")
+    data = np.array(
+        [[np.inf, 1.0], [1.0, 2.0], [2.0, 3.0], [3.0, 4.0], [4.0, 5.0], [5, np.inf]],
+        dtype="float64",
+    )
+    labels = np.array([0, 1, 0, 1, 0, 1], dtype="int64")
+
+    group_mean(actual, counts, data, labels, is_datetimelike=False)
+
+    expected = np.array([[np.inf, 3], [3, np.inf]], dtype="float64")
+
+    tm.assert_numpy_array_equal(
+        actual,
+        expected,
+    )