(* http://www.cs.nyu.edu/courses/summer07/G22.2110-001/hw08-sml-example.txt
   Rename this file into statistics.sml. *)

fun real_square x : real = x * x;

fun list_sum []     = 0.0
|   list_sum (h::t) = h + list_sum t;

fun arithmetic_mean x = list_sum x / real(length x);

fun standard_deviation_helper ([]  , _) = 0.0
|   standard_deviation_helper (h::t, m) = real_square (h - m)
                                          + standard_deviation_helper (t, m);

fun standard_deviation x =
    let val n = length x
        val m = arithmetic_mean x
    in  Math.sqrt (standard_deviation_helper (x, m) / real(n))
    end;

fun input_list_of_real stream =
    let val dummy = print ("Please enter a floating point number, "
                           ^ "or an empty line to end the list: ")
        val str = valOf (TextIO.inputLine stream)
        val opt = Real.fromString (substring (str, 0, size str - 1))
    in
        case opt of SOME r => r :: (input_list_of_real stream)
                  | NONE   => []
    end;

let val l = input_list_of_real TextIO.stdIn
    val a = arithmetic_mean l
    val s = standard_deviation l
in  print ("arithmetic mean: " ^ (Real.toString a) ^ ", "
           ^ "standard deviation: " ^ (Real.toString s) ^ "\n")
end;