; Return the median of the numbers in values, a list of numbers.
(define (median-by-sorting values)
  (list-ref (sort values) (half-length values)) )

; Return the result of sorting the values in the list L.
(define (sort L)
  (accumulate
    insert
    (cons (list (first L)) (rest L)) ) )

; Return the list of numbers in the values list that are less than
; or equal to x. x is a number, values is a list of numbers.
(define (smaller+equal-vals L x)
  (keep-if (lambda (y) (<= y x)) L) )

; Return the list of numbers in the values list that are larger than x.
; x is a number, values is a list of numbers.
(define (larger-vals L x)
  (keep-if (lambda (y) (> y x)) L) )

; L is a sorted list.  Return the result of inserting x into L
; in proper order.
(define (insert L x)
  (append
    (smaller+equal-vals L x)
    (list x)
    (larger-vals L x) ) )