Getting variance and standard deviation in BigQuery

hacker_news_standard_deviation.sql

SELECT
  variance,
  standard_deviation,
  input
FROM (standardDeviation(
    SELECT
      '[' + GROUP_CONCAT_UNQUOTED(STRING(score)) + ']' AS json_array_input
    FROM (
      SELECT
        score
      FROM
        [bigquery-public-data:hacker_news.full_201510]
      WHERE
        score IS NOT NULL
      ORDER BY
        id
      LIMIT
        10)))

hacker_news_standard_deviation_bq.sql

SELECT
  VARIANCE(score),
  STDDEV(score),
  AVG(score)
FROM
  [bigquery-public-data:hacker_news.full_201510]
WHERE
  score IS NOT NULL
LIMIT
  10

standard_udf.js

/**
 * Gets the average of an array of numbers
 * @param {array} arr - An array of numbers
 * @return {number} The average
 */
function average(arr) {
  var sum = 0;
  arr.forEach(function(element, index, array) { sum += element; });
  return sum * 1.0 / arr.length;
}

/**
 * Subtract the mean from each element in an array, then square each
 * Where x is an element in the array, the result is(x - mean)^2
 * @param {array} arr - An array of numbers
 * @return {array} Array of modified numbers
 */
function getDifferenceSquares(arr, mean) {
    var ret = [];
    arr.forEach(function(element, index, array) {
        ret[index] = Math.pow((element - mean), 2); });
    return ret;
}

function standardDeviation(row, emit) {
    var ints = JSON.parse(row.json_array_input);
    var mean = average(ints);
    var variance = average(getDifferenceSquares(ints, mean));
    emit({variance: variance,
          standard_deviation: Math.sqrt(variance),
          input: row.json_array_input});
}

bigquery.defineFunction(
    'standardDeviation',
    ['json_array_input'],
    [{'name': 'variance', 'type': 'float'},
    {'name': 'standard_deviation', 'type': 'float'},
    {'name': 'input', 'type': 'string'}],
    standardDeviation
);