(defconstant e (exp 1))

(defun sum (l)
  (let ((n 0))
    (dolist (one l n) (incf n one))))

(defun mean (l)
  (let ((n 0) (sum 0))
    (dolist (one l (/ sum n))
      (incf sum one)
      (incf n))))

(defun harmonic-mean (x y)  (/ (* 2 x y) (+ x y)))

(defun weighted-sum (l total)
  (sum (mapcar
        #'(lambda (one) 
            (let ((freq   (first one))
                  (weight (rest one)))
              (* (/ freq total) weight)))
        l)))

(defun stdev (n sum sumSq) 
  (sqrt (/ (- sumSq(/ (* sum sum) n)) (- n 1))))

(defun list2stdev (l)
  (let ((n 0) (sum 0) (sumSq 0))
    (dolist (x l (stdev n sum sumSq))
      (incf n)
      (incf sum x)
      (incf sumSq (* x x )))))

(defun median (nums) 
  (labels ((mean (x y) (/ (+ x y ) 2)))
    (let* ((n1         (sort nums #'<))
	   (l          (length n1))
	   (mid        (floor (/ l 2)))
	   (midval     (nth mid  n1))
	   (25percent  (nth (floor (* l 0.25)) n1))
	   (75percent  (nth (floor (* l 0.75)) n1))
	   (50percent  (if (oddp l) 
			   midval
			   (mean midval (nth (- mid 1) n1)))))	 
      (values 50percent
              (- 75percent 50percent)
              75percent
              25percent))))

(defun between (a b c)  (<= a b c))

;(deftest test-stats ()
;  (let ((nums '(1 1 1 1 2 2 4 100)))
;    (check
;      (= 112 (sum nums))
;      (= 3/2 (median nums))
;      (= 14  (mean nums)))))