diff --git a/openmc/stats/univariate.py b/openmc/stats/univariate.py
index de8d08dedb..64627a4e1e 100644
--- a/openmc/stats/univariate.py
+++ b/openmc/stats/univariate.py
@@ -857,7 +857,6 @@ class Tabular(Univariate):
                                       'or linear-linear interpolation.')
         if self.interpolation == 'linear-linear':
             mean = 0.0
-            self.normalize()
             for i in range(1, len(self.x)):
                 y_min = self.p[i-1]
                 y_max = self.p[i]
@@ -872,9 +871,13 @@ class Tabular(Univariate):
                 mean += exp_val
 
         elif self.interpolation == 'histogram':
-            mean = 0.5 * (self.x[:-1] + self.x[1:])
-            mean *= np.diff(self.cdf())
-            mean = sum(mean)
+            x_l = self.x[:-1]
+            x_r = self.x[1:]
+            p_l = self.p[:-1]
+            mean = (0.5 * (x_l + x_r) * (x_r - x_l) * p_l).sum()
+
+        # Normalize for when integral of distribution is not 1
+        mean /= self.integral()
 
         return mean
 
diff --git a/tests/unit_tests/test_stats.py b/tests/unit_tests/test_stats.py
index 378e1fc0ba..ea8898c1a6 100644
--- a/tests/unit_tests/test_stats.py
+++ b/tests/unit_tests/test_stats.py
@@ -166,7 +166,7 @@ def test_watt():
 
 def test_tabular():
     x = np.array([0.0, 5.0, 7.0])
-    p = np.array([0.1, 0.2, 0.05])
+    p = np.array([10.0, 20.0, 5.0])
     d = openmc.stats.Tabular(x, p, 'linear-linear')
     elem = d.to_xml_element('distribution')
 
@@ -178,19 +178,22 @@ def test_tabular():
 
     # test linear-linear sampling
     d = openmc.stats.Tabular(x, p)
-
     n_samples = 100_000
     samples = d.sample(n_samples)
     assert_sample_mean(samples, d.mean())
 
-    # test histogram sampling
-    d = openmc.stats.Tabular(x, p, interpolation='histogram')
+    # test linear-linear normalization
     d.normalize()
     assert d.integral() == pytest.approx(1.0)
 
+    # test histogram sampling
+    d = openmc.stats.Tabular(x, p, interpolation='histogram')
     samples = d.sample(n_samples)
     assert_sample_mean(samples, d.mean())
 
+    d.normalize()
+    assert d.integral() == pytest.approx(1.0)
+
 
 def test_legendre():
     # Pu239 elastic scattering at 100 keV