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:

(defn stateful-std-deviation[x]
  (letfn [(std-dev[x]
            (let [v (deref (find-var (symbol (str *ns* "/v"))))]
              (swap! v conj x)
              (let [m (/ (reduce + @v) (count @v))]
                (Math/sqrt (/ (reduce + (map #(* (- m %) (- m %)) @v)) (count @v))))))]
    (when (nil? (resolve 'v))
      (intern *ns* 'v (atom [])))
    (std-dev x)))