diff --git a/homeassistant/components/sensor/statistics.py b/homeassistant/components/sensor/statistics.py
index a6932e2aebb..19281d36d88 100644
--- a/homeassistant/components/sensor/statistics.py
+++ b/homeassistant/components/sensor/statistics.py
@@ -175,15 +175,20 @@ class StatisticsSensor(Entity):
             self._purge_old()
 
         if not self.is_binary:
-            try:
+            try:  # require only one data point
                 self.mean = round(statistics.mean(self.states), 2)
                 self.median = round(statistics.median(self.states), 2)
+            except statistics.StatisticsError as err:
+                _LOGGER.error(err)
+                self.mean = self.median = STATE_UNKNOWN
+
+            try:  # require at least two data points
                 self.stdev = round(statistics.stdev(self.states), 2)
                 self.variance = round(statistics.variance(self.states), 2)
             except statistics.StatisticsError as err:
                 _LOGGER.error(err)
-                self.mean = self.median = STATE_UNKNOWN
                 self.stdev = self.variance = STATE_UNKNOWN
+
             if self.states:
                 self.total = round(sum(self.states), 2)
                 self.min = min(self.states)
diff --git a/tests/components/sensor/test_statistics.py b/tests/components/sensor/test_statistics.py
index bfb8fb61f9b..48ebf720633 100644
--- a/tests/components/sensor/test_statistics.py
+++ b/tests/components/sensor/test_statistics.py
@@ -3,7 +3,8 @@ import unittest
 import statistics
 
 from homeassistant.setup import setup_component
-from homeassistant.const import (ATTR_UNIT_OF_MEASUREMENT, TEMP_CELSIUS)
+from homeassistant.const import (
+    ATTR_UNIT_OF_MEASUREMENT, TEMP_CELSIUS, STATE_UNKNOWN)
 from homeassistant.util import dt as dt_util
 from tests.common import get_test_home_assistant
 from unittest.mock import patch
@@ -106,6 +107,38 @@ class TestStatisticsSensor(unittest.TestCase):
         self.assertEqual(3.8, state.attributes.get('min_value'))
         self.assertEqual(14, state.attributes.get('max_value'))
 
+    def test_sampling_size_1(self):
+        """Test validity of stats requiring only one sample."""
+        assert setup_component(self.hass, 'sensor', {
+            'sensor': {
+                'platform': 'statistics',
+                'name': 'test',
+                'entity_id': 'sensor.test_monitored',
+                'sampling_size': 1,
+            }
+        })
+
+        for value in self.values[-3:]:  # just the last 3 will do
+            self.hass.states.set('sensor.test_monitored', value,
+                                 {ATTR_UNIT_OF_MEASUREMENT: TEMP_CELSIUS})
+            self.hass.block_till_done()
+
+        state = self.hass.states.get('sensor.test_mean')
+
+        # require only one data point
+        self.assertEqual(self.values[-1], state.attributes.get('min_value'))
+        self.assertEqual(self.values[-1], state.attributes.get('max_value'))
+        self.assertEqual(self.values[-1], state.attributes.get('mean'))
+        self.assertEqual(self.values[-1], state.attributes.get('median'))
+        self.assertEqual(self.values[-1], state.attributes.get('total'))
+        self.assertEqual(0, state.attributes.get('change'))
+        self.assertEqual(0, state.attributes.get('average_change'))
+
+        # require at least two data points
+        self.assertEqual(STATE_UNKNOWN, state.attributes.get('variance'))
+        self.assertEqual(STATE_UNKNOWN,
+                         state.attributes.get('standard_deviation'))
+
     def test_max_age(self):
         """Test value deprecation."""
         mock_data = {