SQLite 3.27

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
CREATE TABLE car_table(Car TEXT, Mileage REAL);
✓
INSERT INTO car_table VALUES
('Toyota', 11.4), 
('Honda', 12.3), 
('Honda', 11.4), 
('Toyota', 6.7), 
('Toyota', 9.8);
✓
SELECT DISTINCT Car,
       AVG(
         CASE counter % 2
           WHEN 0 THEN CASE WHEN rn IN (counter / 2, counter / 2 + 1) THEN mileage END 
           WHEN 1 THEN CASE WHEN rn = counter / 2 + 1 THEN mileage END
         END
       ) OVER (PARTITION BY car) median 
FROM (        
  SELECT *,
         ROW_NUMBER() OVER (PARTITION BY car ORDER BY mileage) rn,
         COUNT(*) OVER (PARTITION BY car) counter
  FROM car_table
)  


Car
median


Honda
11.850000000000001

Toyota
9.8


SELECT DISTINCT Car,
       AVG(CASE WHEN rn IN (counter / 2 + 1, counter / 2 + 1 - (counter % 2 = 0)) THEN mileage END) 
       OVER (PARTITION BY car) median 
FROM (        
  SELECT *,
         ROW_NUMBER() OVER (PARTITION BY car ORDER BY mileage) rn,
         COUNT(*) OVER (PARTITION BY car) counter
  FROM car_table
) 


Car
median


Honda
11.850000000000001

Toyota
9.8