MIT 6.001                                                   Fall 1997

                              QUIZ 2 GRADES

(define q2-grades
                                        ;0-20th percentile:
 '(16 18 19 21 22 23 23 23 25 25.5 26 28 28.5 29.5 30 31.5 32 32 33 34 36
   36 36.5 37 38 39 39.5 40.5 40.5 40.5 41 41 42
                                        ;;20-40th percentile:
   42 43 43 43 44 44.5 45.5 46.5 47 47 48 48 48 48.5 48.5 49.5 50 50 50.5
   50.5 51 53 53 53 53.5 54 54 55 55 55.5 55.5 56 56
                                        ;;40-60th percentile:
   56.5 56.5 56.5 56.5 57 57 57 57 57.5 57.5 57.5 57.5 58 58 58 58 58.5 59 60
   60 60 61.5 61.5 62 62.5 63.5 63.5 63.5 64 64 64 64.5 64.5
                                        ;;60-80th percentile:
   65 65 65.6 66 66 67 67.5 68 68 68.5 69 70 70 70 71 72.5 72.5 73.5 74 74 75
   75.7 76.5 77 77.5 77.5 78.5 78.5 79 79 79 79 79.5
                                        ;;80-100th percentile:
   80 80.5 80.5 81 81 82 82 82.5 83 83 83 84 84 85 85 85 86 86 86 86.5 86.5
   87 88.5 89 89 90 91.5 91.5 93 93 93 93.5 100))


(define n (length q2-grades))
n
;Value: 165

(define av (/ (apply + q2-grades) n))
av
;Value: 59.9260606060606

(define med (list-ref q2-grades (floor (/ n 2))))
med
;Value: 58.5

(define square (lambda (x) (* x x)))

(define (deviation n sum sum-of-sq)
  (sqrt (- (/ sum-of-sq n) (square (/ sum n)))))

(define dev
  (deviation n (apply + q2-grades) (apply + (map square q2-grades))))
dev
;Value: 19.61774057039282