diff --git a/CHANGELOG.md b/CHANGELOG.md
index a8e7621186..cc3a68d8b0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,9 @@
 
 ## unreleased
 
+* [BUGFIX] PromQL: Fix stddev+stdvar aggregations to always ignore native histograms. #14941
+* [BUGFIX] PromQL: Fix stddev+stdvar aggregations to treat Infinity consistently. #14941
+
 ## 3.0.0-beta.1 / 2024-10-09
 
 * [CHANGE] regexp `.` now matches all characters (performance improvement). #14505
diff --git a/promql/engine.go b/promql/engine.go
index 60b4b81384..5435db0fc4 100644
--- a/promql/engine.go
+++ b/promql/engine.go
@@ -2926,7 +2926,15 @@ func (ev *evaluator) aggregation(e *parser.AggregateExpr, q float64, inputMatrix
 					group.hasHistogram = true
 				}
 			case parser.STDVAR, parser.STDDEV:
-				group.floatValue = 0
+				switch {
+				case h != nil:
+					// Ignore histograms for STDVAR and STDDEV.
+					group.seen = false
+				case math.IsNaN(f), math.IsInf(f, 0):
+					group.floatValue = math.NaN()
+				default:
+					group.floatValue = 0
+				}
 			case parser.QUANTILE:
 				group.heap = make(vectorByValueHeap, 1)
 				group.heap[0] = Sample{F: f}
diff --git a/promql/promqltest/testdata/aggregators.test b/promql/promqltest/testdata/aggregators.test
index 3c91883960..e2eb381dbc 100644
--- a/promql/promqltest/testdata/aggregators.test
+++ b/promql/promqltest/testdata/aggregators.test
@@ -572,3 +572,160 @@ clear
 #
 #eval instant at 1m count(topk(1,max(up) without()) == topk(1,max(up) without()) == topk(1,max(up) without()) == topk(1,max(up) without()) == topk(1,max(up) without()))
 #	{} 1
+
+clear
+
+# Test stddev produces consistent results regardless the order the data is loaded in.
+load 5m
+	series{label="a"} 1
+	series{label="b"} 2
+	series{label="c"} {{schema:1 sum:15 count:10 buckets:[3 2 5 7 9]}}
+
+eval instant at 0m stddev(series)
+	{} 0.5
+
+eval instant at 0m stdvar(series)
+	{} 0.25
+
+eval instant at 0m stddev by (label) (series)
+	{label="a"} 0
+	{label="b"} 0
+
+eval instant at 0m stdvar by (label) (series)
+	{label="a"} 0
+	{label="b"} 0
+
+clear
+
+load 5m
+	series{label="a"} {{schema:1 sum:15 count:10 buckets:[3 2 5 7 9]}}
+	series{label="b"} 1
+	series{label="c"} 2
+
+eval instant at 0m stddev(series)
+	{} 0.5
+
+eval instant at 0m stdvar(series)
+	{} 0.25
+
+eval instant at 0m stddev by (label) (series)
+	{label="b"} 0
+	{label="c"} 0
+
+eval instant at 0m stdvar by (label) (series)
+	{label="b"} 0
+	{label="c"} 0
+
+clear
+
+load 5m
+	series{label="a"} 1
+	series{label="b"} 2
+	series{label="c"} NaN
+
+eval instant at 0m stddev(series)
+	{} NaN
+
+eval instant at 0m stdvar(series)
+	{} NaN
+
+eval instant at 0m stddev by (label) (series)
+	{label="a"} 0
+	{label="b"} 0
+	{label="c"} NaN
+
+eval instant at 0m stdvar by (label) (series)
+	{label="a"} 0
+	{label="b"} 0
+	{label="c"} NaN
+
+clear
+
+load 5m
+	series{label="a"} NaN
+	series{label="b"} 1
+	series{label="c"} 2
+
+eval instant at 0m stddev(series)
+	{} NaN
+
+eval instant at 0m stdvar(series)
+	{} NaN
+
+eval instant at 0m stddev by (label) (series)
+	{label="a"} NaN
+	{label="b"} 0
+	{label="c"} 0
+
+eval instant at 0m stdvar by (label) (series)
+	{label="a"} NaN
+	{label="b"} 0
+	{label="c"} 0
+
+clear
+
+load 5m
+	series NaN
+
+eval instant at 0m stddev(series)
+	{} NaN
+
+eval instant at 0m stdvar(series)
+	{} NaN
+
+clear
+
+load 5m
+	series{label="a"} 1
+	series{label="b"} 2
+	series{label="c"} inf
+
+eval instant at 0m stddev (series)
+	{} NaN
+
+eval instant at 0m stdvar (series)
+	{} NaN
+
+eval instant at 0m stddev by (label) (series)
+	{label="a"} 0
+	{label="b"} 0
+	{label="c"} NaN
+
+eval instant at 0m stdvar by (label) (series)
+	{label="a"} 0
+	{label="b"} 0
+	{label="c"} NaN
+
+clear
+
+load 5m
+	series{label="a"} inf
+	series{label="b"} 1
+	series{label="c"} 2
+
+eval instant at 0m stddev(series)
+	{} NaN
+
+eval instant at 0m stdvar(series)
+	{} NaN
+
+eval instant at 0m stddev by (label) (series)
+	{label="a"} NaN
+	{label="b"} 0
+	{label="c"} 0
+
+eval instant at 0m stdvar by (label) (series)
+	{label="a"} NaN
+	{label="b"} 0
+	{label="c"} 0
+
+clear
+
+load 5m
+	series inf
+
+eval instant at 0m stddev(series)
+	{} NaN
+
+eval instant at 0m stdvar(series)
+	{} NaN