(* CSE 230 W02 midterm average and variance *)

fun sum(L : real list) = foldr (op +) 0.0 L;

val reall = map real;

fun grademid L = real(hd(hd(L)));

val grm = map grademid;

fun avg L = sum L / real(length L);

fun var L = let val a = avg L; fun f(R : real) = (R - a)*(R - a) in
    Real.Math.sqrt(sum(map f L)) end;

print "\n end of definitions \n\n";

use "gradefile";

print "\n now the computations: \n\n";

val allgrades = g1 @ g2 @ g3 @ g4;
val average = avg(grm(allgrades));
val variance = var(grm(allgrades));