Learning AI: csx72 » Sum, mean, median of numbers

Sum, mean, median of numbers

This is a Lisp page, written Sat Jan 19 15:21:54 PST 2008.

LISP functions can accept any number of arguments after the "&rest" keyword. So, to add up any number of "nums":

(defun sum (&rest nums)
  (let ((sum 0))
    (dolist (one nums sum)
      (incf sum one))))

E.g.

(SUM 1 1 1 1 2 2 4 100) => 112

And, if you want the mean value, divide the sum by the number of items in the list:

(defun mean (&rest nums)
  (let ((sum 0)
        (n   0))
    (dolist (one nums (/ sum n))
      (incf n)
      (incf sum one))))

E.g.

(MEAN 1 1 1 1 2 2 4 100) => 14

LISP functions can also return more than one value using the "values" keyword. Here, we compute mean and standard deviation of a set of numbers.

(defun mean-sd (&rest nums)
  (let ((sum 0)
        (n   0)
        (sumSq 0))
    (labels ((mean () (/ sum n))
             (sd   () (sqrt (/ (- sumSq(/ (* sum sum) n)) (- n 1) ))))
      (dolist (one nums)
         (incf n)
         (incf sum   one)
         (incf sumSq (* one one)))
      (values 
       (mean) 
       (sd)))))

E.g.

(MEAN-sd 1 1 1 1 2 2 4 100) => 14 34.764515

We can use the same kind of function to return the median and the "spread" of a set of numbers. The median value is the point at which half the values lie below it:

If a sorted list of numbers is of odd size, it is just the middle value.
However of that list is of even size, then it is some number in between the middle two values.

This list also returns "spread", i.e. the difference between the 50% and 75% value. "Spread" (not the official technical name) is useful for measuring the expected deviation from the median.

(defun median (&rest nums) 
  "return 50% and (75-50)% values"
  (let* ((n1         (sort nums #'<))
         (l          (length n1))
         (mid        (floor (/ l 2)))
         (midval     (nth mid  n1))
         (75percent  (nth (floor (* l 0.75)) n1))
         (50percent  (if (oddp l) 
                         midval
                         (mean midval (nth (- mid 1) n1)))))    
    (values  
     50percent
     (- 75percent 
        50percent))))

E.g.

(MEDIAN 1 1 1 1 2 2 4 100) => 3/2 5/2

Sum, mean, median of numbers

cs472 / cs572