diff --git a/homeassistant/components/statistics/sensor.py b/homeassistant/components/statistics/sensor.py
index bc6acb2732a..ac62b63e8ca 100644
--- a/homeassistant/components/statistics/sensor.py
+++ b/homeassistant/components/statistics/sensor.py
@@ -64,8 +64,12 @@ STAT_CHANGE = "change"
 STAT_CHANGE_SAMPLE = "change_sample"
 STAT_CHANGE_SECOND = "change_second"
 STAT_COUNT = "count"
+STAT_COUNT_BINARY_ON = "count_on"
+STAT_COUNT_BINARY_OFF = "count_off"
 STAT_DATETIME_NEWEST = "datetime_newest"
 STAT_DATETIME_OLDEST = "datetime_oldest"
+STAT_DATETIME_VALUE_MAX = "datetime_value_max"
+STAT_DATETIME_VALUE_MIN = "datetime_value_min"
 STAT_DISTANCE_95P = "distance_95_percent_of_values"
 STAT_DISTANCE_99P = "distance_99_percent_of_values"
 STAT_DISTANCE_ABSOLUTE = "distance_absolute"
@@ -99,6 +103,8 @@ STATS_NUMERIC_SUPPORT = {
     STAT_COUNT,
     STAT_DATETIME_NEWEST,
     STAT_DATETIME_OLDEST,
+    STAT_DATETIME_VALUE_MAX,
+    STAT_DATETIME_VALUE_MIN,
     STAT_DISTANCE_95P,
     STAT_DISTANCE_99P,
     STAT_DISTANCE_ABSOLUTE,
@@ -118,18 +124,26 @@ STATS_BINARY_SUPPORT = {
     STAT_AVERAGE_STEP,
     STAT_AVERAGE_TIMELESS,
     STAT_COUNT,
+    STAT_COUNT_BINARY_ON,
+    STAT_COUNT_BINARY_OFF,
+    STAT_DATETIME_NEWEST,
+    STAT_DATETIME_OLDEST,
     STAT_MEAN,
 }
 
 STATS_NOT_A_NUMBER = {
     STAT_DATETIME_NEWEST,
     STAT_DATETIME_OLDEST,
+    STAT_DATETIME_VALUE_MAX,
+    STAT_DATETIME_VALUE_MIN,
     STAT_QUANTILES,
 }
 
 STATS_DATETIME = {
     STAT_DATETIME_NEWEST,
     STAT_DATETIME_OLDEST,
+    STAT_DATETIME_VALUE_MAX,
+    STAT_DATETIME_VALUE_MIN,
 }
 
 # Statistics which retain the unit of the source entity
@@ -351,7 +365,7 @@ class StatisticsSensor(SensorEntity):
         except ValueError:
             self.attributes[STAT_SOURCE_VALUE_VALID] = False
             _LOGGER.error(
-                "%s: parsing error, expected number and received %s",
+                "%s: parsing error. Expected number or binary state, but received '%s'",
                 self.entity_id,
                 new_state.state,
             )
@@ -370,7 +384,11 @@ class StatisticsSensor(SensorEntity):
             unit = base_unit
         elif self._state_characteristic in STATS_NOT_A_NUMBER:
             unit = None
-        elif self._state_characteristic == STAT_COUNT:
+        elif self._state_characteristic in (
+            STAT_COUNT,
+            STAT_COUNT_BINARY_ON,
+            STAT_COUNT_BINARY_OFF,
+        ):
             unit = None
         elif self._state_characteristic == STAT_VARIANCE:
             unit = base_unit + "²"
@@ -614,6 +632,16 @@ class StatisticsSensor(SensorEntity):
             return self.ages[0]
         return None
 
+    def _stat_datetime_value_max(self) -> datetime | None:
+        if len(self.states) > 0:
+            return self.ages[self.states.index(max(self.states))]
+        return None
+
+    def _stat_datetime_value_min(self) -> datetime | None:
+        if len(self.states) > 0:
+            return self.ages[self.states.index(min(self.states))]
+        return None
+
     def _stat_distance_95_percent_of_values(self) -> StateType:
         if len(self.states) >= 2:
             return 2 * 1.96 * cast(float, self._stat_standard_deviation())
@@ -704,6 +732,18 @@ class StatisticsSensor(SensorEntity):
     def _stat_binary_count(self) -> StateType:
         return len(self.states)
 
+    def _stat_binary_count_on(self) -> StateType:
+        return self.states.count(True)
+
+    def _stat_binary_count_off(self) -> StateType:
+        return self.states.count(False)
+
+    def _stat_binary_datetime_newest(self) -> datetime | None:
+        return self._stat_datetime_newest()
+
+    def _stat_binary_datetime_oldest(self) -> datetime | None:
+        return self._stat_datetime_oldest()
+
     def _stat_binary_mean(self) -> StateType:
         if len(self.states) > 0:
             return 100.0 / len(self.states) * self.states.count(True)
diff --git a/tests/components/statistics/test_sensor.py b/tests/components/statistics/test_sensor.py
index dbcb3b1b8e7..56255216f52 100644
--- a/tests/components/statistics/test_sensor.py
+++ b/tests/components/statistics/test_sensor.py
@@ -687,6 +687,22 @@ async def test_state_characteristics(hass: HomeAssistant):
             "value_9": (start_datetime + timedelta(minutes=1)).isoformat(),
             "unit": None,
         },
+        {
+            "source_sensor_domain": "sensor",
+            "name": "datetime_value_max",
+            "value_0": STATE_UNKNOWN,
+            "value_1": (start_datetime + timedelta(minutes=9)).isoformat(),
+            "value_9": (start_datetime + timedelta(minutes=2)).isoformat(),
+            "unit": None,
+        },
+        {
+            "source_sensor_domain": "sensor",
+            "name": "datetime_value_min",
+            "value_0": STATE_UNKNOWN,
+            "value_1": (start_datetime + timedelta(minutes=9)).isoformat(),
+            "value_9": (start_datetime + timedelta(minutes=5)).isoformat(),
+            "unit": None,
+        },
         {
             "source_sensor_domain": "sensor",
             "name": "distance_95_percent_of_values",
@@ -811,6 +827,38 @@ async def test_state_characteristics(hass: HomeAssistant):
             "value_9": len(VALUES_BINARY),
             "unit": None,
         },
+        {
+            "source_sensor_domain": "binary_sensor",
+            "name": "count_on",
+            "value_0": 0,
+            "value_1": 1,
+            "value_9": VALUES_BINARY.count("on"),
+            "unit": None,
+        },
+        {
+            "source_sensor_domain": "binary_sensor",
+            "name": "count_off",
+            "value_0": 0,
+            "value_1": 0,
+            "value_9": VALUES_BINARY.count("off"),
+            "unit": None,
+        },
+        {
+            "source_sensor_domain": "binary_sensor",
+            "name": "datetime_newest",
+            "value_0": STATE_UNKNOWN,
+            "value_1": (start_datetime + timedelta(minutes=9)).isoformat(),
+            "value_9": (start_datetime + timedelta(minutes=9)).isoformat(),
+            "unit": None,
+        },
+        {
+            "source_sensor_domain": "binary_sensor",
+            "name": "datetime_oldest",
+            "value_0": STATE_UNKNOWN,
+            "value_1": (start_datetime + timedelta(minutes=9)).isoformat(),
+            "value_9": (start_datetime + timedelta(minutes=1)).isoformat(),
+            "unit": None,
+        },
         {
             "source_sensor_domain": "binary_sensor",
             "name": "mean",