fix: report standard medians for even benchmark samples

cmd/autocar/bench.go

@@ -256,10 +256,19 @@ func populateAccelerationMetadata(output *benchOutput, mode byte, dialer transpo
 	}
 }
 
+// percentile expects sorted, nonnegative measurements. The median averages
+// both central values for even sample counts; tail percentiles retain the
+// nearest-order-statistic convention instead of interpolating observations.
 func percentile(sorted []float64, fraction float64) float64 {
 	if len(sorted) == 0 {
 		return 0
 	}
+	if fraction == 0.5 && len(sorted)%2 == 0 {
+		middle := len(sorted) / 2
+		lower, upper := sorted[middle-1], sorted[middle]
+		// Avoid overflowing the sum for large, finite measurements.
+		return lower + (upper-lower)/2
+	}
 	index := int(float64(len(sorted)-1)*fraction + 0.5)
 	if index < 0 {
 		index = 0

cmd/autocar/bench_median_test.go

@@ -0,0 +1,38 @@
+package main
+
+import (
+	"math"
+	"testing"
+)
+
+func TestPercentileMedian(t *testing.T) {
+	for _, tc := range []struct {
+		name   string
+		sorted []float64
+		want   float64
+	}{
+		{"empty", nil, 0},
+		{"single", []float64{3}, 3},
+		{"two", []float64{2, 10}, 6},
+		{"four", []float64{1, 2, 8, 100}, 5},
+		{"odd", []float64{1, 3, 100}, 3},
+		{"repeated", []float64{4, 4, 4, 4}, 4},
+		{"large", []float64{math.MaxFloat64, math.MaxFloat64}, math.MaxFloat64},
+	} {
+		t.Run(tc.name, func(t *testing.T) {
+			if got := percentile(tc.sorted, 0.5); got != tc.want {
+				t.Fatalf("median(%v) = %v, want %v", tc.sorted, got, tc.want)
+			}
+		})
+	}
+}
+
+func TestPercentileTailConventionUnchanged(t *testing.T) {
+	values := []float64{2, 10}
+	if got := percentile(values, 0.05); got != 2 {
+		t.Fatalf("p05 = %v, want 2", got)
+	}
+	if got := percentile(values, 0.95); got != 10 {
+		t.Fatalf("p95 = %v, want 10", got)
+	}
+}

docs/BENCHMARK.md

@@ -30,6 +30,12 @@ Measure direct and tunneled paths with the same payload, warmup and iterations:
 JSON contains raw `results_mbps` and `durations_ms`, plus `median_mbps`,
 `p05_mbps`, `p95_mbps`, `median_duration_ms` and `p95_duration_ms`. The throughput
 p95 is the upper tail; use throughput p05 or duration p95 to discuss slow runs.
+Both medians use the middle observation for an odd sample count and the average
+of the two middle observations for an even count. Tail percentiles retain the
+nearest order statistic at index `round((n-1)*p)` (zero-based); they do not
+interpolate and are descriptive summaries, not confidence bounds. Older builds
+used that rounded index for medians too, selecting the upper middle observation
+for even counts. Recompute from raw samples when comparing those reports.
 The selected transport and sender metadata must remain identical across all
 measured iterations or the command fails. `transport` is the requested policy
 (`auto`, `quic`, `tls` or `direct`); `selected_transport` records the actual