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id	title	challengeType	forumTopicId	dashedName
5a23c84252665b21eecc7e03	Cumulative standard deviation	1	302240	cumulative-standard-deviation

--description--

Suppose that the entire population of interest is eight students in a particular class. For a finite set of numbers, the population standard deviation is found by taking the square root of the average of the squared deviations of the values subtracted from their average value. The marks of a class of eight students (that is, a statistical population) are the following eight values:

2, 4, 4, 4, 5, 5, 7, 9

These eight data points have the mean (average) of 5:

\mu ={\frac {2+4+4+4+5+5+7+9}{8}}={\frac {40}{8}}=5

First, calculate the deviations of each data point from the mean, and square the result of each:

Deviations of each data	Square the result
`(2-5)^{2}=(-3)^{2}=9`	`(5-5)^{2}=0^{2}=0`
`(4-5)^{2}=(-1)^{2}=1`	`(5-5)^{2}=0^{2}=0`
`(4-5)^{2}=(-1)^{2}=1`	`(7-5)^{2}=2^{2}=4`
`(4-5)^{2}=(-1)^{2}=1`	`(9-5)^{2}=4^{2}=16`

The variance is the mean of these values:

\sigma ^{2}={\frac {9+1+1+1+0+0+4+16}{8}}={\frac {32}{8}}=4

and the population standard deviation is equal to the square root of the variance:

\sigma ={\sqrt {4}}=2

Write a function that takes an array of numbers as parameter and returns the standard deviation of the series.

--hints--

standardDeviation should be a function.

assert(typeof standardDeviation == 'function');

standardDeviation([2, 4, 4, 4, 5, 5, 7, 9]) should return a number.

assert(typeof standardDeviation([2, 4, 4, 4, 5, 5, 7, 9]) == 'number');

standardDeviation([2, 4, 4, 4, 5, 5, 7, 9]) should return 2.

assert.equal(standardDeviation([2, 4, 4, 4, 5, 5, 7, 9]), 2);

standardDeviation([600, 470, 170, 430, 300]) should return 147.323.

assert.equal(standardDeviation([600, 470, 170, 430, 300]), 147.323);

standardDeviation([75, 83, 96, 100, 121, 125]) should return 18.239.

assert.equal(standardDeviation([75, 83, 96, 100, 121, 125]), 18.239);

standardDeviation([23, 37, 45, 49, 56, 63, 63, 70, 72, 82]) should return 16.87.

assert.equal(
  standardDeviation([23, 37, 45, 49, 56, 63, 63, 70, 72, 82]),
  16.87
);

standardDeviation([271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287, 314]) should return 22.631.

assert.equal(
  standardDeviation([
    271,
    354,
    296,
    301,
    333,
    326,
    285,
    298,
    327,
    316,
    287,
    314
  ]),
  22.631
);

--seed--

--seed-contents--

function standardDeviation(arr) {

}

--solutions--

function standardDeviation(arr) {
  var sum = 0,
    sum_sq = 0,
    n = arr.length;
  arr.forEach(function(e) {
    sum += e;
    sum_sq += e * e;
  });

  var std_dev = Math.sqrt(sum_sq / n - Math.pow(sum / n, 2));
  return Math.round(std_dev * 1000) / 1000;
}

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