Add max_age to statistics sensor (#8790)

* Add max_age to statistics sensor

* Allow only non-zero sampling sizes

* Fix long line

* Fix style

tests/components/sensor/test_statistics.py

@@ -4,7 +4,10 @@ import statistics
 
 from homeassistant.setup import setup_component
 from homeassistant.const import (ATTR_UNIT_OF_MEASUREMENT, TEMP_CELSIUS)
+from homeassistant.util import dt as dt_util
 from tests.common import get_test_home_assistant
+from unittest.mock import patch
+from datetime import datetime, timedelta
 
 
 class TestStatisticsSensor(unittest.TestCase):
@@ -100,3 +103,35 @@ class TestStatisticsSensor(unittest.TestCase):
 
         self.assertEqual(3.8, state.attributes.get('min_value'))
         self.assertEqual(14, state.attributes.get('max_value'))
+
+    def test_max_age(self):
+        """Test value deprecation."""
+        mock_data = {
+            'return_time': datetime(2017, 8, 2, 12, 23, tzinfo=dt_util.UTC),
+        }
+
+        def mock_now():
+            return mock_data['return_time']
+
+        with patch('homeassistant.components.sensor.statistics.dt_util.utcnow',
+                   new=mock_now):
+            assert setup_component(self.hass, 'sensor', {
+                'sensor': {
+                    'platform': 'statistics',
+                    'name': 'test',
+                    'entity_id': 'sensor.test_monitored',
+                    'max_age': {'minutes': 3}
+                }
+            })
+
+            for value in self.values:
+                self.hass.states.set('sensor.test_monitored', value,
+                                     {ATTR_UNIT_OF_MEASUREMENT: TEMP_CELSIUS})
+                self.hass.block_till_done()
+                # insert the next value one minute later
+                mock_data['return_time'] += timedelta(minutes=1)
+
+            state = self.hass.states.get('sensor.test_mean')
+
+        self.assertEqual(6, state.attributes.get('min_value'))
+        self.assertEqual(14, state.attributes.get('max_value'))