TSQL Seleccione la fila Min &Max al agrupar

Puede hacerlo de inmediato usando funciones de ventana :

; with ordering as (
  SELECT max([Range]) AS 'Range'
     , count(ID) AS 'Count'
     , round(avg([Profit]), 2) AS 'AVG Profit'
     , row_number() over (order by avg([Profit])) rn_min
     , row_number() over (order by avg([Profit]) desc) rn_max
    FROM
        Orders
    GROUP BY
        Range_begining
    HAVING COUNT(ID) > 10
)
select [range], [count], [avg profit],
       case when rn_max = 1 
            then 'Max profit'
            else 'Min profit'
        end Description
  from ordering
 where (rn_max = 1 or rn_min = 1)

Y aquí está el ejemplo de Sql Fiddle .