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:

procedure main()

stddev() # reset state / empty
every  s := stddev(![2,4,4,4,5,5,7,9]) do
   write("stddev (so far) := ",s)

end

procedure stddev(x)  # running standard deviation
static X,sumX,sum2X

   if /x then {   # reset state
      X := []
      sumX := sum2X := 0.
      }
   else {         # accumulate
      put(X,x)
      sumX +:= x
      sum2X +:= x^2
      return sqrt( (sum2X / *X) - (sumX / *X)^2 )
      }
end