text: //     wink-statistics
  //     Fast and Numerically Stable Statistical Analysis Utilities.
  //
  //     Copyright (C) GRAYPE Systems Private Limited
  //
  //     This file is part of “wink-statistics”.
  //
  //     Permission is hereby granted, free of charge, to any person obtaining a
  //     copy of this software and associated documentation files (the "Software"),
  //     to deal in the Software without restriction, including without limitation
  //     the rights to use, copy, modify, merge, publish, distribute, sublicense,
  //     and/or sell copies of the Software, and to permit persons to whom the
  //     Software is furnished to do so, subject to the following conditions:
  //
  //     The above copyright notice and this permission notice shall be included
  //     in all copies or substantial portions of the Software.
  //
  //     THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  //     OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  //     FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
  //     THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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  //     FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
  //     DEALINGS IN THE SOFTWARE.
  
  // ## streaming
  
  // Load accessor.
  var value = require( './accessor.js' );
  // Load wink helpers for validation.
  var helpers = require( 'wink-helpers' );
  
  // ### varianceXn
  /**
   * Comuptes the population `variance * size` of numbers contained in the `x` array.
   * The computations are inspired by the method proposed by [B. P. Welford](http://dx.doi.org/10.1080/00401706.1962.10490022).
   *
   * @private
   *
   * @param {array} x array containing 1 or more elements.
   * @param {(string|number|function)} [accessor=undefined] required when elements of
   * `x` are objects or arrays instead of numbers.
   * For objects, use key (string) to access the value; in case of arrays, use
   * index (number) to access the value; or it could be a function
   * that extracts the value from the element passed to it.
   * @return {object} containing `varianceXn` and `size`.
   *
   * @example
   * varianceXN( [ 2, 3, 5, 7 ] );
   * // returns { varianceXn: 14.749999999999998, size: 4 }
   */
  var varianceXn = function ( x, accessor ) {
    var mean = 0;
    var varianceXn1 = 0;
    var prevMean;
    var i, imax, xi;
    var obj = Object.create( null );
  
    if ( !helpers.array.isArray( x ) || !x.length ) {
      throw Error( 'data-variance: x should be an array of length > 0, instead found: ' + JSON.stringify( x ) );
    }
  
    for ( i = 0, imax = x.length; i < imax; i += 1 ) {
      xi = value( x[ i ], accessor );
      prevMean = mean;
      mean += ( xi - mean ) / ( i + 1 );
      varianceXn1 += ( xi - prevMean ) * ( xi - mean );
    }
  
    obj.varianceXn = varianceXn1;
    obj.size = imax;
    return obj;
  }; // varianceXn()
  
  module.exports = varianceXn;
  