Problem Statement

Write a stateful function, class, generator or co-routine that takes a series of floating point numbers, one at a time, and returns the running standard deviation of the series. The task implementation should use the most natural programming style of those listed for the function in the implementation language; the task must state which is being used. Do not apply Bessel's correction; the returned standard deviation should always be computed as if the sample seen so far is the entire population.

Use this to compute the standard deviation of this demonstration set,

{ 2 , 4 , 4 , 4 , 5 , 5 , 7 , 9 }

{\displaystyle {2,4,4,4,5,5,7,9}}

, which is

2

{\displaystyle 2}

.

Let's start with the solution:

let sqr x = x *. x

let stddev l =
  let n, sx, sx2 =
    List.fold_left
      (fun (n, sx, sx2) x -> succ n, sx +. x, sx2 +. sqr x)
      (0, 0., 0.) l
  in
  sqrt ((sx2 -. sqr sx /. float n) /. float n)

let _ =
  let l = [ 2.;4.;4.;4.;5.;5.;7.;9. ] in
  Printf.printf "List: ";
  List.iter (Printf.printf "%g  ") l;
  Printf.printf "\nStandard deviation: %g\n" (stddev l)