diff --git a/datafusion/expr-common/src/signature.rs b/datafusion/expr-common/src/signature.rs
index 54bb84f03d3d5..4c766b2cc50c9 100644
--- a/datafusion/expr-common/src/signature.rs
+++ b/datafusion/expr-common/src/signature.rs
@@ -1585,6 +1585,7 @@ mod tests {
                 vec![DataType::UInt16, DataType::UInt16],
                 vec![DataType::UInt32, DataType::UInt32],
                 vec![DataType::UInt64, DataType::UInt64],
+                vec![DataType::Float16, DataType::Float16],
                 vec![DataType::Float32, DataType::Float32],
                 vec![DataType::Float64, DataType::Float64]
             ]
diff --git a/datafusion/expr-common/src/type_coercion/aggregates.rs b/datafusion/expr-common/src/type_coercion/aggregates.rs
index 01d093950d471..ab4d086e4ca5f 100644
--- a/datafusion/expr-common/src/type_coercion/aggregates.rs
+++ b/datafusion/expr-common/src/type_coercion/aggregates.rs
@@ -42,6 +42,7 @@ pub static NUMERICS: &[DataType] = &[
     DataType::UInt16,
     DataType::UInt32,
     DataType::UInt64,
+    DataType::Float16,
     DataType::Float32,
     DataType::Float64,
 ];
diff --git a/datafusion/expr/src/type_coercion/functions.rs b/datafusion/expr/src/type_coercion/functions.rs
index e6a1b53418e67..d1c0940aeb306 100644
--- a/datafusion/expr/src/type_coercion/functions.rs
+++ b/datafusion/expr/src/type_coercion/functions.rs
@@ -851,10 +851,13 @@ fn coerced_from<'a>(
         (UInt16, Null | UInt8 | UInt16) => Some(type_into.clone()),
         (UInt32, Null | UInt8 | UInt16 | UInt32) => Some(type_into.clone()),
         (UInt64, Null | UInt8 | UInt16 | UInt32 | UInt64) => Some(type_into.clone()),
+        (Float16, Null | Int8 | Int16 | UInt8 | UInt16 | Float16) => {
+            Some(type_into.clone())
+        }
         (
             Float32,
             Null | Int8 | Int16 | Int32 | Int64 | UInt8 | UInt16 | UInt32 | UInt64
-            | Float32,
+            | Float16 | Float32,
         ) => Some(type_into.clone()),
         (
             Float64,
@@ -867,6 +870,7 @@ fn coerced_from<'a>(
             | UInt16
             | UInt32
             | UInt64
+            | Float16
             | Float32
             | Float64
             | Decimal32(_, _)
diff --git a/datafusion/optimizer/src/analyzer/type_coercion.rs b/datafusion/optimizer/src/analyzer/type_coercion.rs
index 5ce2c3b6af6a6..63fed1f82c5dc 100644
--- a/datafusion/optimizer/src/analyzer/type_coercion.rs
+++ b/datafusion/optimizer/src/analyzer/type_coercion.rs
@@ -1929,7 +1929,7 @@ mod test {
             .err()
             .unwrap()
             .strip_backtrace();
-        assert!(err.starts_with("Error during planning: Failed to coerce arguments to satisfy a call to 'avg' function: coercion from Utf8 to the signature Uniform(1, [Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Float32, Float64]) failed"));
+        assert!(err.starts_with("Error during planning: Failed to coerce arguments to satisfy a call to 'avg' function: coercion from Utf8 to the signature Uniform(1, [Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Float16, Float32, Float64]) failed"));
         Ok(())
     }
 
diff --git a/datafusion/sqllogictest/test_files/aggregate.slt b/datafusion/sqllogictest/test_files/aggregate.slt
index 036bb93283cc6..8b641e02efc25 100644
--- a/datafusion/sqllogictest/test_files/aggregate.slt
+++ b/datafusion/sqllogictest/test_files/aggregate.slt
@@ -571,6 +571,16 @@ SELECT covar(c2, c12) FROM aggregate_test_100
 ----
 -0.079969012479
 
+query R
+SELECT covar_pop(arrow_cast(c2, 'Float16'), arrow_cast(c12, 'Float16')) FROM aggregate_test_100
+----
+-0.079163311005
+
+query R
+SELECT covar(arrow_cast(c2, 'Float16'), arrow_cast(c12, 'Float16')) FROM aggregate_test_100
+----
+-0.079962940409
+
 # single_row_query_covar_1
 query R
 select covar_samp(sq.column1, sq.column2) from (values (1.1, 2.2)) as sq
@@ -1313,6 +1323,24 @@ select approx_median(arrow_cast(col_f32, 'Float16')), arrow_typeof(approx_median
 ----
 2.75 Float16
 
+# This shouldn't be NaN, see:
+# https://github.com/apache/datafusion/issues/18945
+query RT
+select
+  percentile_cont(0.5) within group (order by arrow_cast(col_f32, 'Float16')),
+  arrow_typeof(percentile_cont(0.5) within group (order by arrow_cast(col_f32, 'Float16')))
+from median_table;
+----
+NaN Float16
+
+query RT
+select
+  approx_percentile_cont(0.5) within group (order by arrow_cast(col_f32, 'Float16')),
+  arrow_typeof(approx_percentile_cont(0.5) within group (order by arrow_cast(col_f32, 'Float16')))
+from median_table;
+----
+2.75 Float16
+
 query ?T
 select approx_median(NULL), arrow_typeof(approx_median(NULL)) from median_table;
 ----
@@ -6718,7 +6746,12 @@ from aggregate_test_100;
 ----
 0.051534002628 0.48427355347 100 0.001929150558 0.479274948239 0.508972509913 6.707779292571 9.234223721582 0.345678715695
 
-
+query R
+select
+    regr_slope(arrow_cast(c12, 'Float16'), arrow_cast(c11, 'Float16'))
+from aggregate_test_100;
+----
+0.051477733249
 
 # regr_*() functions ignore NULLs
 query RRIRRRRRR