; functions for finding the statistics of a list of numbers
; All functions assume they are given a list of numbers and return a number
; Some functions need minimum of one number in the list and some at least two.
; Qualities:  these a simple demonstartion that are not designed to be fast 
;	or accurate
(define (square x) (* x x))

(define ( sumsquares x) ( sum (squares x) ))

(define ( squaresum x) ( square (sum x) ))


(define ( sd x) (sqrt(float (var x)))); sd means standard deviation

(define ( mean x) ( / (sum x) (length x) ))

(define ( var x) ; var is the variance of the numbers in the list
	(/ 	(- (sumsquares x) 
		   (/ (squaresum x) 
	              (length x)
		   )
		) 
		(- (length x) 1
		)
	);/
);define

; Our LISP has length predefined
; (define (length x) 
;	(if (null x) 0 (1+ (length (cdr x)))
;	)
;)

(define (sum x); add up the items in a list
	( if (null x) 0 (+ (car x) (sum (cdr x)))
	)
)

(define ( squares x) ; replace each number in list by its square
	( if (null x) NIL (cons (square(car x)) (squares(cdr x))))
)