alamb commented on code in PR #3009:
URL: https://github.com/apache/arrow-datafusion/pull/3009#discussion_r937114037


##########
datafusion/physical-expr/src/aggregate/median.rs:
##########
@@ -0,0 +1,260 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+//! # Median
+
+use crate::expressions::format_state_name;
+use crate::{AggregateExpr, PhysicalExpr};
+use arrow::array::{
+    Array, ArrayRef, Float32Array, Float64Array, Int16Array, Int32Array, 
Int64Array,
+    Int8Array, PrimitiveArray, PrimitiveBuilder, UInt16Array, UInt32Array, 
UInt64Array,
+    UInt8Array,
+};
+use arrow::compute::sort;
+use arrow::datatypes::{ArrowPrimitiveType, DataType, Field};
+use datafusion_common::{DataFusionError, Result, ScalarValue};
+use datafusion_expr::{Accumulator, AggregateState};
+use std::any::Any;
+use std::sync::Arc;
+
+/// MEDIAN aggregate expression. This uses a lot of memory because all values 
need to be
+/// stored in memory before a result can be computed. If an approximation is 
sufficient
+/// then APPROX_MEDIAN provides a much more efficient solution.
+#[derive(Debug)]
+pub struct Median {
+    name: String,
+    expr: Arc<dyn PhysicalExpr>,
+    data_type: DataType,
+}
+
+impl Median {
+    /// Create a new MEDIAN aggregate function
+    pub fn new(
+        expr: Arc<dyn PhysicalExpr>,
+        name: impl Into<String>,
+        data_type: DataType,
+    ) -> Self {
+        Self {
+            name: name.into(),
+            expr,
+            data_type,
+        }
+    }
+}
+
+impl AggregateExpr for Median {
+    /// Return a reference to Any that can be used for downcasting
+    fn as_any(&self) -> &dyn Any {
+        self
+    }
+
+    fn field(&self) -> Result<Field> {
+        Ok(Field::new(&self.name, self.data_type.clone(), true))
+    }
+
+    fn create_accumulator(&self) -> Result<Box<dyn Accumulator>> {
+        Ok(Box::new(MedianAccumulator {
+            data_type: self.data_type.clone(),
+            all_values: vec![],
+        }))
+    }
+
+    fn state_fields(&self) -> Result<Vec<Field>> {
+        Ok(vec![Field::new(
+            &format_state_name(&self.name, "median"),
+            self.data_type.clone(),
+            true,
+        )])
+    }
+
+    fn expressions(&self) -> Vec<Arc<dyn PhysicalExpr>> {
+        vec![self.expr.clone()]
+    }
+
+    fn name(&self) -> &str {
+        &self.name
+    }
+}
+
+#[derive(Debug)]
+struct MedianAccumulator {
+    data_type: DataType,
+    all_values: Vec<ArrayRef>,

Review Comment:
   I wonder if you would be better served here by using an ArrayBuilder (though 
I realize they are strongly typed so it might be more award -- though it is 
likely faster)



##########
datafusion/physical-expr/src/aggregate/median.rs:
##########
@@ -0,0 +1,260 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+//! # Median
+
+use crate::expressions::format_state_name;
+use crate::{AggregateExpr, PhysicalExpr};
+use arrow::array::{
+    Array, ArrayRef, Float32Array, Float64Array, Int16Array, Int32Array, 
Int64Array,
+    Int8Array, PrimitiveArray, PrimitiveBuilder, UInt16Array, UInt32Array, 
UInt64Array,
+    UInt8Array,
+};
+use arrow::compute::sort;
+use arrow::datatypes::{ArrowPrimitiveType, DataType, Field};
+use datafusion_common::{DataFusionError, Result, ScalarValue};
+use datafusion_expr::{Accumulator, AggregateState};
+use std::any::Any;
+use std::sync::Arc;
+
+/// MEDIAN aggregate expression. This uses a lot of memory because all values 
need to be
+/// stored in memory before a result can be computed. If an approximation is 
sufficient
+/// then APPROX_MEDIAN provides a much more efficient solution.
+#[derive(Debug)]
+pub struct Median {
+    name: String,
+    expr: Arc<dyn PhysicalExpr>,
+    data_type: DataType,
+}
+
+impl Median {
+    /// Create a new MEDIAN aggregate function
+    pub fn new(
+        expr: Arc<dyn PhysicalExpr>,
+        name: impl Into<String>,
+        data_type: DataType,
+    ) -> Self {
+        Self {
+            name: name.into(),
+            expr,
+            data_type,
+        }
+    }
+}
+
+impl AggregateExpr for Median {
+    /// Return a reference to Any that can be used for downcasting
+    fn as_any(&self) -> &dyn Any {
+        self
+    }
+
+    fn field(&self) -> Result<Field> {
+        Ok(Field::new(&self.name, self.data_type.clone(), true))
+    }
+
+    fn create_accumulator(&self) -> Result<Box<dyn Accumulator>> {
+        Ok(Box::new(MedianAccumulator {
+            data_type: self.data_type.clone(),
+            all_values: vec![],
+        }))
+    }
+
+    fn state_fields(&self) -> Result<Vec<Field>> {
+        Ok(vec![Field::new(
+            &format_state_name(&self.name, "median"),
+            self.data_type.clone(),
+            true,
+        )])
+    }
+
+    fn expressions(&self) -> Vec<Arc<dyn PhysicalExpr>> {
+        vec![self.expr.clone()]
+    }
+
+    fn name(&self) -> &str {
+        &self.name
+    }
+}
+
+#[derive(Debug)]
+struct MedianAccumulator {
+    data_type: DataType,
+    all_values: Vec<ArrayRef>,
+}
+
+macro_rules! median {
+    ($SELF:ident, $TY:ty, $SCALAR_TY:ident, $TWO:expr) => {{
+        let combined = combine_arrays::<$TY>($SELF.all_values.as_slice())?;
+        if combined.is_empty() {
+            return Ok(ScalarValue::Null);
+        }
+        let sorted = sort(&combined, None)?;
+        let array = sorted
+            .as_any()
+            .downcast_ref::<PrimitiveArray<$TY>>()
+            .ok_or(DataFusionError::Internal(
+                "median! macro failed to cast array to expected 
type".to_string(),
+            ))?;
+        let len = sorted.len();
+        let mid = len / 2;
+        if len % 2 == 0 {
+            Ok(ScalarValue::$SCALAR_TY(Some(
+                (array.value(mid - 1) + array.value(mid)) / $TWO,
+            )))
+        } else {
+            Ok(ScalarValue::$SCALAR_TY(Some(array.value(mid))))
+        }
+    }};
+}
+
+impl Accumulator for MedianAccumulator {
+    fn state(&self) -> Result<Vec<AggregateState>> {
+        let mut vec: Vec<AggregateState> = self
+            .all_values
+            .iter()
+            .map(|v| AggregateState::Array(v.clone()))
+            .collect();
+        if vec.is_empty() {
+            match self.data_type {

Review Comment:
   Is it correct to produce a single `[0]` element array? Wouldn't that mean 
that the 0 is now included in the median calculation even though it was not in 
the original data?



##########
datafusion/physical-expr/src/aggregate/utils.rs:
##########
@@ -0,0 +1,48 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+//! Utilities used in aggregates

Review Comment:
   👍 



##########
datafusion/physical-expr/src/aggregate/median.rs:
##########
@@ -0,0 +1,260 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+//! # Median
+
+use crate::expressions::format_state_name;
+use crate::{AggregateExpr, PhysicalExpr};
+use arrow::array::{
+    Array, ArrayRef, Float32Array, Float64Array, Int16Array, Int32Array, 
Int64Array,
+    Int8Array, PrimitiveArray, PrimitiveBuilder, UInt16Array, UInt32Array, 
UInt64Array,
+    UInt8Array,
+};
+use arrow::compute::sort;
+use arrow::datatypes::{ArrowPrimitiveType, DataType, Field};
+use datafusion_common::{DataFusionError, Result, ScalarValue};
+use datafusion_expr::{Accumulator, AggregateState};
+use std::any::Any;
+use std::sync::Arc;
+
+/// MEDIAN aggregate expression. This uses a lot of memory because all values 
need to be
+/// stored in memory before a result can be computed. If an approximation is 
sufficient
+/// then APPROX_MEDIAN provides a much more efficient solution.
+#[derive(Debug)]
+pub struct Median {
+    name: String,
+    expr: Arc<dyn PhysicalExpr>,
+    data_type: DataType,
+}
+
+impl Median {
+    /// Create a new MEDIAN aggregate function
+    pub fn new(
+        expr: Arc<dyn PhysicalExpr>,
+        name: impl Into<String>,
+        data_type: DataType,
+    ) -> Self {
+        Self {
+            name: name.into(),
+            expr,
+            data_type,
+        }
+    }
+}
+
+impl AggregateExpr for Median {
+    /// Return a reference to Any that can be used for downcasting
+    fn as_any(&self) -> &dyn Any {
+        self
+    }
+
+    fn field(&self) -> Result<Field> {
+        Ok(Field::new(&self.name, self.data_type.clone(), true))
+    }
+
+    fn create_accumulator(&self) -> Result<Box<dyn Accumulator>> {
+        Ok(Box::new(MedianAccumulator {
+            data_type: self.data_type.clone(),
+            all_values: vec![],
+        }))
+    }
+
+    fn state_fields(&self) -> Result<Vec<Field>> {
+        Ok(vec![Field::new(
+            &format_state_name(&self.name, "median"),
+            self.data_type.clone(),
+            true,
+        )])
+    }
+
+    fn expressions(&self) -> Vec<Arc<dyn PhysicalExpr>> {
+        vec![self.expr.clone()]
+    }
+
+    fn name(&self) -> &str {
+        &self.name
+    }
+}
+
+#[derive(Debug)]
+struct MedianAccumulator {
+    data_type: DataType,
+    all_values: Vec<ArrayRef>,
+}
+
+macro_rules! median {
+    ($SELF:ident, $TY:ty, $SCALAR_TY:ident, $TWO:expr) => {{
+        let combined = combine_arrays::<$TY>($SELF.all_values.as_slice())?;
+        if combined.is_empty() {
+            return Ok(ScalarValue::Null);
+        }
+        let sorted = sort(&combined, None)?;
+        let array = sorted
+            .as_any()
+            .downcast_ref::<PrimitiveArray<$TY>>()
+            .ok_or(DataFusionError::Internal(
+                "median! macro failed to cast array to expected 
type".to_string(),
+            ))?;
+        let len = sorted.len();
+        let mid = len / 2;
+        if len % 2 == 0 {
+            Ok(ScalarValue::$SCALAR_TY(Some(
+                (array.value(mid - 1) + array.value(mid)) / $TWO,
+            )))
+        } else {
+            Ok(ScalarValue::$SCALAR_TY(Some(array.value(mid))))
+        }
+    }};
+}
+
+impl Accumulator for MedianAccumulator {
+    fn state(&self) -> Result<Vec<AggregateState>> {
+        let mut vec: Vec<AggregateState> = self
+            .all_values
+            .iter()
+            .map(|v| AggregateState::Array(v.clone()))
+            .collect();
+        if vec.is_empty() {
+            match self.data_type {
+                DataType::UInt8 => vec.push(AggregateState::Array(Arc::new(
+                    UInt8Array::from_value(0_u8, 0),
+                ))),
+                DataType::UInt16 => vec.push(AggregateState::Array(Arc::new(
+                    UInt16Array::from_value(0_u16, 0),
+                ))),
+                DataType::UInt32 => vec.push(AggregateState::Array(Arc::new(
+                    UInt32Array::from_value(0_u32, 0),
+                ))),
+                DataType::UInt64 => vec.push(AggregateState::Array(Arc::new(
+                    UInt64Array::from_value(0_u64, 0),
+                ))),
+                DataType::Int8 => vec.push(AggregateState::Array(Arc::new(
+                    Int8Array::from_value(0_i8, 0),
+                ))),
+                DataType::Int16 => vec.push(AggregateState::Array(Arc::new(
+                    Int16Array::from_value(0_i16, 0),
+                ))),
+                DataType::Int32 => vec.push(AggregateState::Array(Arc::new(
+                    Int32Array::from_value(0_i32, 0),
+                ))),
+                DataType::Int64 => vec.push(AggregateState::Array(Arc::new(
+                    Int64Array::from_value(0_i64, 0),
+                ))),
+                DataType::Float32 => vec.push(AggregateState::Array(Arc::new(
+                    Float32Array::from_value(0_f32, 0),
+                ))),
+                DataType::Float64 => vec.push(AggregateState::Array(Arc::new(
+                    Float64Array::from_value(0_f64, 0),
+                ))),
+                _ => {
+                    return Err(DataFusionError::Execution(
+                        "unsupported data type for median".to_string(),
+                    ))
+                }
+            }
+        }
+        Ok(vec)
+    }
+
+    fn update_batch(&mut self, values: &[ArrayRef]) -> Result<()> {
+        let x = values[0].clone();
+        self.all_values.extend_from_slice(&[x]);
+        Ok(())
+    }
+
+    fn merge_batch(&mut self, states: &[ArrayRef]) -> Result<()> {
+        for array in states {
+            self.all_values.extend_from_slice(&[array.clone()]);
+        }
+        Ok(())
+    }
+
+    fn evaluate(&self) -> Result<ScalarValue> {
+        match self.all_values[0].data_type() {
+            DataType::Int8 => median!(self, arrow::datatypes::Int8Type, Int8, 
2),
+            DataType::Int16 => median!(self, arrow::datatypes::Int16Type, 
Int16, 2),
+            DataType::Int32 => median!(self, arrow::datatypes::Int32Type, 
Int32, 2),
+            DataType::Int64 => median!(self, arrow::datatypes::Int64Type, 
Int64, 2),
+            DataType::UInt8 => median!(self, arrow::datatypes::UInt8Type, 
UInt8, 2),
+            DataType::UInt16 => median!(self, arrow::datatypes::UInt16Type, 
UInt16, 2),
+            DataType::UInt32 => median!(self, arrow::datatypes::UInt32Type, 
UInt32, 2),
+            DataType::UInt64 => median!(self, arrow::datatypes::UInt64Type, 
UInt64, 2),
+            DataType::Float32 => {
+                median!(self, arrow::datatypes::Float32Type, Float32, 2_f32)
+            }
+            DataType::Float64 => {
+                median!(self, arrow::datatypes::Float64Type, Float64, 2_f64)
+            }
+            _ => Err(DataFusionError::Execution(
+                "unsupported data type for median".to_string(),
+            )),
+        }
+    }
+}
+
+/// Combine all non-null values from provided arrays into a single array
+fn combine_arrays<T: ArrowPrimitiveType>(arrays: &[ArrayRef]) -> 
Result<ArrayRef> {

Review Comment:
   You might be able to do this with `concat` and `take` as well
   
   Untested
   ```rust
   let final_array = concat(arrays);
   let indexes = final_array.iter().enumerate().filter_map(|(i, v)| v.map(|_| 
i)).collect();
   take(final_array, indexes)
   ```



##########
datafusion/physical-expr/src/aggregate/median.rs:
##########
@@ -0,0 +1,260 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+//! # Median
+
+use crate::expressions::format_state_name;
+use crate::{AggregateExpr, PhysicalExpr};
+use arrow::array::{
+    Array, ArrayRef, Float32Array, Float64Array, Int16Array, Int32Array, 
Int64Array,
+    Int8Array, PrimitiveArray, PrimitiveBuilder, UInt16Array, UInt32Array, 
UInt64Array,
+    UInt8Array,
+};
+use arrow::compute::sort;
+use arrow::datatypes::{ArrowPrimitiveType, DataType, Field};
+use datafusion_common::{DataFusionError, Result, ScalarValue};
+use datafusion_expr::{Accumulator, AggregateState};
+use std::any::Any;
+use std::sync::Arc;
+
+/// MEDIAN aggregate expression. This uses a lot of memory because all values 
need to be
+/// stored in memory before a result can be computed. If an approximation is 
sufficient
+/// then APPROX_MEDIAN provides a much more efficient solution.
+#[derive(Debug)]
+pub struct Median {
+    name: String,
+    expr: Arc<dyn PhysicalExpr>,
+    data_type: DataType,
+}
+
+impl Median {
+    /// Create a new MEDIAN aggregate function
+    pub fn new(
+        expr: Arc<dyn PhysicalExpr>,
+        name: impl Into<String>,
+        data_type: DataType,
+    ) -> Self {
+        Self {
+            name: name.into(),
+            expr,
+            data_type,
+        }
+    }
+}
+
+impl AggregateExpr for Median {
+    /// Return a reference to Any that can be used for downcasting
+    fn as_any(&self) -> &dyn Any {
+        self
+    }
+
+    fn field(&self) -> Result<Field> {
+        Ok(Field::new(&self.name, self.data_type.clone(), true))
+    }
+
+    fn create_accumulator(&self) -> Result<Box<dyn Accumulator>> {
+        Ok(Box::new(MedianAccumulator {
+            data_type: self.data_type.clone(),
+            all_values: vec![],
+        }))
+    }
+
+    fn state_fields(&self) -> Result<Vec<Field>> {
+        Ok(vec![Field::new(
+            &format_state_name(&self.name, "median"),
+            self.data_type.clone(),
+            true,
+        )])
+    }
+
+    fn expressions(&self) -> Vec<Arc<dyn PhysicalExpr>> {
+        vec![self.expr.clone()]
+    }
+
+    fn name(&self) -> &str {
+        &self.name
+    }
+}
+
+#[derive(Debug)]
+struct MedianAccumulator {
+    data_type: DataType,
+    all_values: Vec<ArrayRef>,
+}
+
+macro_rules! median {
+    ($SELF:ident, $TY:ty, $SCALAR_TY:ident, $TWO:expr) => {{
+        let combined = combine_arrays::<$TY>($SELF.all_values.as_slice())?;
+        if combined.is_empty() {
+            return Ok(ScalarValue::Null);
+        }
+        let sorted = sort(&combined, None)?;
+        let array = sorted
+            .as_any()
+            .downcast_ref::<PrimitiveArray<$TY>>()
+            .ok_or(DataFusionError::Internal(
+                "median! macro failed to cast array to expected 
type".to_string(),
+            ))?;
+        let len = sorted.len();
+        let mid = len / 2;
+        if len % 2 == 0 {
+            Ok(ScalarValue::$SCALAR_TY(Some(
+                (array.value(mid - 1) + array.value(mid)) / $TWO,
+            )))
+        } else {
+            Ok(ScalarValue::$SCALAR_TY(Some(array.value(mid))))
+        }
+    }};
+}
+
+impl Accumulator for MedianAccumulator {
+    fn state(&self) -> Result<Vec<AggregateState>> {
+        let mut vec: Vec<AggregateState> = self
+            .all_values
+            .iter()
+            .map(|v| AggregateState::Array(v.clone()))
+            .collect();
+        if vec.is_empty() {
+            match self.data_type {
+                DataType::UInt8 => vec.push(AggregateState::Array(Arc::new(
+                    UInt8Array::from_value(0_u8, 0),
+                ))),
+                DataType::UInt16 => vec.push(AggregateState::Array(Arc::new(
+                    UInt16Array::from_value(0_u16, 0),
+                ))),
+                DataType::UInt32 => vec.push(AggregateState::Array(Arc::new(
+                    UInt32Array::from_value(0_u32, 0),
+                ))),
+                DataType::UInt64 => vec.push(AggregateState::Array(Arc::new(
+                    UInt64Array::from_value(0_u64, 0),
+                ))),
+                DataType::Int8 => vec.push(AggregateState::Array(Arc::new(
+                    Int8Array::from_value(0_i8, 0),
+                ))),
+                DataType::Int16 => vec.push(AggregateState::Array(Arc::new(
+                    Int16Array::from_value(0_i16, 0),
+                ))),
+                DataType::Int32 => vec.push(AggregateState::Array(Arc::new(
+                    Int32Array::from_value(0_i32, 0),
+                ))),
+                DataType::Int64 => vec.push(AggregateState::Array(Arc::new(
+                    Int64Array::from_value(0_i64, 0),
+                ))),
+                DataType::Float32 => vec.push(AggregateState::Array(Arc::new(
+                    Float32Array::from_value(0_f32, 0),
+                ))),
+                DataType::Float64 => vec.push(AggregateState::Array(Arc::new(
+                    Float64Array::from_value(0_f64, 0),
+                ))),
+                _ => {
+                    return Err(DataFusionError::Execution(
+                        "unsupported data type for median".to_string(),
+                    ))
+                }
+            }
+        }
+        Ok(vec)
+    }
+
+    fn update_batch(&mut self, values: &[ArrayRef]) -> Result<()> {
+        let x = values[0].clone();
+        self.all_values.extend_from_slice(&[x]);
+        Ok(())
+    }
+
+    fn merge_batch(&mut self, states: &[ArrayRef]) -> Result<()> {
+        for array in states {
+            self.all_values.extend_from_slice(&[array.clone()]);
+        }
+        Ok(())
+    }
+
+    fn evaluate(&self) -> Result<ScalarValue> {
+        match self.all_values[0].data_type() {
+            DataType::Int8 => median!(self, arrow::datatypes::Int8Type, Int8, 
2),

Review Comment:
   Instead of using a macro here, I wonder if you could use the `concat` and  
`take` kernels 
   
   https://docs.rs/arrow/19.0.0/arrow/compute/kernels/concat/index.html
   https://docs.rs/arrow/19.0.0/arrow/compute/kernels/take/index.html
   
   Something like (untested):
   
   ```rust
   let sorted = sort(concat(&self.all_values));
   let len = sorted.len();
   let mid = len / 2;
   if len % 2 == 0 {
     let indexes: UInt64Array = [mid-1, mid].into_iter().collect();
     // 🤔  Not sure how to do an average:
     let values = average(take(sorted, indexes)) 
     ScalarValue::try_from_array(values, 0)
   } else {
     ScalarValue::try_from_array(sorted, mid)
   } 
   
   ```
   But the need for an `average` stymies that - though I guess we could 
implement an `average` kernel in datafusion and then put it back into arrow



##########
datafusion/core/tests/sql/aggregates.rs:
##########
@@ -221,7 +221,7 @@ async fn csv_query_stddev_6() -> Result<()> {
 }
 
 #[tokio::test]
-async fn csv_query_median_1() -> Result<()> {

Review Comment:
   If possible, I would recommend adding a basic test in sql for a median for 
all the different data types that are supported  (not just on 
aggregate_test_100 but a dedicated test setup with known data (maybe integers 
10, 9, 8, ... 0) 



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