diff --git a/DOCUMENTATION.md b/DOCUMENTATION.md
index a7a75a8..e0b9e24 100644
--- a/DOCUMENTATION.md
+++ b/DOCUMENTATION.md
@@ -2183,6 +2183,9 @@ func Quartile(input Float64Data) (Quartiles, error)
 ```
 Quartile returns the three quartile points from a slice of data
 
+A single value is its own lower hinge, median and upper hinge, so all
+three quartiles are that value.
+
 
 
 
diff --git a/quartile.go b/quartile.go
index 40bbf6e..bd10033 100644
--- a/quartile.go
+++ b/quartile.go
@@ -10,6 +10,9 @@ type Quartiles struct {
 }
 
 // Quartile returns the three quartile points from a slice of data
+//
+// A single value is its own lower hinge, median and upper hinge, so all
+// three quartiles are that value.
 func Quartile(input Float64Data) (Quartiles, error) {
 
 	il := input.Len()
@@ -17,6 +20,14 @@ func Quartile(input Float64Data) (Quartiles, error) {
 		return Quartiles{}, EmptyInputErr
 	}
 
+	// One value is its own quartiles, which also matches what Percentile
+	// returns for that value at any percent. The general path below cannot
+	// produce it: the cutoffs would leave both halves empty and the two
+	// hinges would come back as NaN.
+	if il == 1 {
+		return Quartiles{input[0], input[0], input[0]}, nil
+	}
+
 	// Start by sorting a copy of the slice
 	copy := sortedCopy(input)
 
@@ -32,7 +43,8 @@ func Quartile(input Float64Data) (Quartiles, error) {
 		c2 = c1 + 1
 	}
 
-	// Find the Medians with the cutoff points
+	// Find the Medians with the cutoff points. Both halves hold at least
+	// one value for every length above one, so Median cannot fail here.
 	Q1, _ := Median(copy[:c1])
 	Q2, _ := Median(copy)
 	Q3, _ := Median(copy[c2:])
diff --git a/quartile_test.go b/quartile_test.go
index 93d524e..28fb353 100644
--- a/quartile_test.go
+++ b/quartile_test.go
@@ -41,6 +41,47 @@ func TestQuartile(t *testing.T) {
 	}
 }
 
+func TestQuartile_SingleValue(t *testing.T) {
+	quartiles, err := stats.Quartile([]float64{43})
+	if err != nil {
+		t.Errorf("Should not have returned an error; got %v", err)
+	}
+	if quartiles.Q1 != 43 {
+		t.Errorf("Q1 %v != 43", quartiles.Q1)
+	}
+	if quartiles.Q2 != 43 {
+		t.Errorf("Q2 %v != 43", quartiles.Q2)
+	}
+	if quartiles.Q3 != 43 {
+		t.Errorf("Q3 %v != 43", quartiles.Q3)
+	}
+
+	// The quartiles of one value agree with Percentile on the same value.
+	for _, percent := range []float64{25, 50, 75} {
+		value, err := stats.Percentile([]float64{43}, percent)
+		if err != nil || value != 43 {
+			t.Errorf("Percentile %v on one value: got %v (err %v)", percent, value, err)
+		}
+	}
+}
+
+func TestQuartile_SingleValueDependents(t *testing.T) {
+	iqr, err := stats.InterQuartileRange([]float64{43})
+	if err != nil || iqr != 0 {
+		t.Errorf("IQR of one value: got %v (err %v), want 0", iqr, err)
+	}
+
+	mh, err := stats.Midhinge([]float64{43})
+	if err != nil || mh != 43 {
+		t.Errorf("Midhinge of one value: got %v (err %v), want 43", mh, err)
+	}
+
+	tr, err := stats.Trimean([]float64{43})
+	if err != nil || tr != 43 {
+		t.Errorf("Trimean of one value: got %v (err %v), want 43", tr, err)
+	}
+}
+
 func TestInterQuartileRange(t *testing.T) {
 	s1 := []float64{102, 104, 105, 107, 108, 109, 110, 112, 115, 116, 118}
 	iqr, _ := stats.InterQuartileRange(s1)