diff --git a/homeassistant/components/statistics/sensor.py b/homeassistant/components/statistics/sensor.py
index db50e4249f2..5e28777e673 100644
--- a/homeassistant/components/statistics/sensor.py
+++ b/homeassistant/components/statistics/sensor.py
@@ -79,6 +79,9 @@ STAT_MEDIAN = "median"
 STAT_NOISINESS = "noisiness"
 STAT_QUANTILES = "quantiles"
 STAT_STANDARD_DEVIATION = "standard_deviation"
+STAT_SUM = "sum"
+STAT_SUM_DIFFERENCES = "sum_differences"
+STAT_SUM_DIFFERENCES_NONNEGATIVE = "sum_differences_nonnegative"
 STAT_TOTAL = "total"
 STAT_VALUE_MAX = "value_max"
 STAT_VALUE_MIN = "value_min"
@@ -114,6 +117,9 @@ STATS_NUMERIC_SUPPORT = {
     STAT_NOISINESS,
     STAT_QUANTILES,
     STAT_STANDARD_DEVIATION,
+    STAT_SUM,
+    STAT_SUM_DIFFERENCES,
+    STAT_SUM_DIFFERENCES_NONNEGATIVE,
     STAT_TOTAL,
     STAT_VALUE_MAX,
     STAT_VALUE_MIN,
@@ -160,6 +166,9 @@ STAT_NUMERIC_RETAIN_UNIT = {
     STAT_MEDIAN,
     STAT_NOISINESS,
     STAT_STANDARD_DEVIATION,
+    STAT_SUM,
+    STAT_SUM_DIFFERENCES,
+    STAT_SUM_DIFFERENCES_NONNEGATIVE,
     STAT_TOTAL,
     STAT_VALUE_MAX,
     STAT_VALUE_MIN,
@@ -670,10 +679,7 @@ class StatisticsSensor(SensorEntity):
 
     def _stat_noisiness(self) -> StateType:
         if len(self.states) >= 2:
-            diff_sum = sum(
-                abs(j - i) for i, j in zip(list(self.states), list(self.states)[1:])
-            )
-            return diff_sum / (len(self.states) - 1)
+            return cast(float, self._stat_sum_differences()) / (len(self.states) - 1)
         return None
 
     def _stat_quantiles(self) -> StateType:
@@ -695,11 +701,31 @@ class StatisticsSensor(SensorEntity):
             return statistics.stdev(self.states)
         return None
 
-    def _stat_total(self) -> StateType:
+    def _stat_sum(self) -> StateType:
         if len(self.states) > 0:
             return sum(self.states)
         return None
 
+    def _stat_sum_differences(self) -> StateType:
+        if len(self.states) >= 2:
+            diff_sum = sum(
+                abs(j - i) for i, j in zip(list(self.states), list(self.states)[1:])
+            )
+            return diff_sum
+        return None
+
+    def _stat_sum_differences_nonnegative(self) -> StateType:
+        if len(self.states) >= 2:
+            diff_sum_nn = sum(
+                (j - i if j >= i else j - 0)
+                for i, j in zip(list(self.states), list(self.states)[1:])
+            )
+            return diff_sum_nn
+        return None
+
+    def _stat_total(self) -> StateType:
+        return self._stat_sum()
+
     def _stat_value_max(self) -> StateType:
         if len(self.states) > 0:
             return max(self.states)
diff --git a/tests/components/statistics/test_sensor.py b/tests/components/statistics/test_sensor.py
index 453d07fb69f..691159fe2fc 100644
--- a/tests/components/statistics/test_sensor.py
+++ b/tests/components/statistics/test_sensor.py
@@ -769,6 +769,56 @@ async def test_state_characteristics(hass: HomeAssistant):
             "value_9": float(round(statistics.stdev(VALUES_NUMERIC), 2)),
             "unit": "°C",
         },
+        {
+            "source_sensor_domain": "sensor",
+            "name": "sum",
+            "value_0": STATE_UNKNOWN,
+            "value_1": float(VALUES_NUMERIC[-1]),
+            "value_9": float(sum(VALUES_NUMERIC)),
+            "unit": "°C",
+        },
+        {
+            "source_sensor_domain": "sensor",
+            "name": "sum_differences",
+            "value_0": STATE_UNKNOWN,
+            "value_1": STATE_UNKNOWN,
+            "value_9": float(
+                sum(
+                    [
+                        abs(20 - 17),
+                        abs(15.2 - 20),
+                        abs(5 - 15.2),
+                        abs(3.8 - 5),
+                        abs(9.2 - 3.8),
+                        abs(6.7 - 9.2),
+                        abs(14 - 6.7),
+                        abs(6 - 14),
+                    ]
+                )
+            ),
+            "unit": "°C",
+        },
+        {
+            "source_sensor_domain": "sensor",
+            "name": "sum_differences_nonnegative",
+            "value_0": STATE_UNKNOWN,
+            "value_1": STATE_UNKNOWN,
+            "value_9": float(
+                sum(
+                    [
+                        20 - 17,
+                        15.2 - 0,
+                        5 - 0,
+                        3.8 - 0,
+                        9.2 - 3.8,
+                        6.7 - 0,
+                        14 - 6.7,
+                        6 - 0,
+                    ]
+                )
+            ),
+            "unit": "°C",
+        },
         {
             "source_sensor_domain": "sensor",
             "name": "total",