diff --git a/datafusion/functions-aggregate/src/variance.rs b/datafusion/functions-aggregate/src/variance.rs
index 810247a2884a9..41e0048ba7a9d 100644
--- a/datafusion/functions-aggregate/src/variance.rs
+++ b/datafusion/functions-aggregate/src/variance.rs
@@ -316,6 +316,7 @@ fn merge(
     mean2: f64,
     m22: f64,
 ) -> (u64, f64, f64) {
+    debug_assert!(count != 0 || count2 != 0, "Cannot merge two empty states");
     let new_count = count + count2;
     let new_mean =
         mean * count as f64 / new_count as f64 + mean2 * count2 as f64 / new_count as f64;
@@ -573,6 +574,9 @@ impl GroupsAccumulator for VarianceGroupsAccumulator {
             partial_m2s,
             opt_filter,
             |group_index, partial_count, partial_mean, partial_m2| {
+                if partial_count == 0 {
+                    return;
+                }
                 let (new_count, new_mean, new_m2) = merge(
                     self.counts[group_index],
                     self.means[group_index],
@@ -612,3 +616,32 @@ impl GroupsAccumulator for VarianceGroupsAccumulator {
             + self.counts.capacity() * size_of::<u64>()
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use datafusion_expr::EmitTo;
+
+    use super::*;
+
+    #[test]
+    fn test_groups_accumulator_merge_empty_states() -> Result<()> {
+        let state_1 = vec![
+            Arc::new(UInt64Array::from(vec![0])) as ArrayRef,
+            Arc::new(Float64Array::from(vec![0.0])),
+            Arc::new(Float64Array::from(vec![0.0])),
+        ];
+        let state_2 = vec![
+            Arc::new(UInt64Array::from(vec![2])) as ArrayRef,
+            Arc::new(Float64Array::from(vec![1.0])),
+            Arc::new(Float64Array::from(vec![0.0])),
+        ];
+        let mut acc = VarianceGroupsAccumulator::new(StatsType::Sample);
+        acc.merge_batch(&state_1, &[0], None, 1)?;
+        acc.merge_batch(&state_2, &[0], None, 1)?;
+        let result = acc.evaluate(EmitTo::All)?;
+        let result = result.as_any().downcast_ref::<Float64Array>().unwrap();
+        assert_eq!(result.len(), 1);
+        assert_eq!(result.value(0), 0.0);
+        Ok(())
+    }
+}