Computing Weighted Averages

It's easy to compute a weighted average incorrectly if you're not careful. A weighted average should have the property that if an assignment has a weight of, say 10% of the final grade, it should have that weight whether the assignment is graded on a scale of 100 or a scale of 20.

The following bit of code does the weighted-average algorithm correctly:

;; weighted-average : ListOfNumber ListOfNumber
;; GIVEN: a list of actual scores, a list of maximum possible
;; scores, and a list of  relative weights
;; RETURNS: the weighted average.
;; EXAMPLEs:
;; (weighted-average (list 5 10) (list 10 10) (list 1 1)) = .75
;; (weighted-average (list 5 10) (list 10 10) (list 0 1)) = 1.0
;; strategy: function composition

(define (weighted-average scores maxes weights)
  (let ((weighted-sum
          (sum
            (map
              (lambda (score max weight) (* (/ score max) weight))
              scores maxes weights)))
        (total-weight (sum weights)))
    (/ weighted-sum total-weight)))

;; sum : ListOfNumber -> Number
;; GIVEN a list of numbers,
;; RETURNS: their sum
;; Example:
;; (sum (list 3 4 1)) = 8
;; (sum empty) = 0
;; strategy: higher-order function composition

(define sum
  (lambda (l)
    (foldr + 0 l)))

Last modified: Sun Jan 10 2016