#lang typed/racket

(: sum (-> (Listof Number) Number))
(define (sum list) (foldr + 0 list))

(: mean (-> (Listof Number) Number))
(define (mean sample)
  (/ (sum sample) (length sample)))

(: standard-deviation (-> (Listof Number) Number))
(define (standard-deviation sample)
  (let* ((degrees-of-freedom (- (length sample) 1))
        (sample-mean (mean sample))
        (sum-of-squared-errors (sum (map (lambda (xi) (expt (- xi sample-mean) 2)) sample))))
    (sqrt (/ sum-of-squared-errors degrees-of-freedom))))