# data-boxplot.js

``````//     wink-statistics
//     Fast and Numerically Stable Statistical Analysis Utilities.
//
//     Copyright (C) 2017-18  GRAYPE Systems Private Limited
//
//     This file is part of “wink-statistics”.
//
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//     copy of this software and associated documentation files (the "Software"),
//     to deal in the Software without restriction, including without limitation
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//     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.
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//     OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// ## data

var fiveNumSummary = require( './data-five-num-summary.js' );
var value = require( './accessor.js' );

// ### Boxplot

/**
*
* Performs complete [boxplot](https://en.wikipedia.org/wiki/Box_plot) analysis
* including computation of notches and outliers.
*
* @memberof data
* @param {array} sortedData sorted in ascending order of value.
* @param {number} [coeff=1.5] used for outliers computation.
* @param {(string|number|function)} [accessor=undefined] required when elements of
* `sortedData` 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.
* @returns {object} consisting of `min`, `q1`, `median`, `q3`,
* `max`, `iqr`, `range`, `size` along with `leftNotch`, and `rightNotch`.
* The `leftOutliers/rightOutliers` (object), if present, contains the `count`, `fence`
* and `begin/end` indexes to `sortedData` for easy extraction of exact values.
* @example
* var data = [
*   -12, 14, 14, 14, 16, 18, 20, 20, 21, 23, 27, 27, 27, 29, 31,
*   31, 32, 32, 34, 36, 40, 40, 40, 40, 40, 42, 51, 56, 60, 88
* ];
* boxplot( data );
* returns {
* //   min: -12, q1: 20, median: 31, q3: 40, max: 88,
* //   iqr: 20, range: 100, size: 30,
* //   leftOutliers: { begin: 0, end: 0, count: 1, fence: 14 },
* //   rightOutliers: { begin: 29, end: 29, count: 1, fence: 60 },
* //   leftNotch: 25.230655727612252,
* //   rightNotch: 36.76934427238775
* // }
*/
var boxplot = function ( sortedData, coeff, accessor ) {
var fns = fiveNumSummary( sortedData, accessor );
var coef = Math.abs( coeff || 1.5 );
var i;
var iqrXcoef = fns.iqr * coef;
var leftFence = fns.q1 - iqrXcoef;
var leftOutliers, rightOutliers;
var rightFence = fns.q3 + iqrXcoef;

var ci = ( 1.58 * fns.iqr ) / ( Math.sqrt( fns.size ) );
// Compute outliers only and only if `iqrXcoef` is greater than `0`, because
// with `iqrXcoef` as `0`, fences will become `q1` and `q3` respectively!
if ( iqrXcoef > 0 ) {
// Compute Left outliers, if any.
for ( i = 0; value( sortedData[ i ], accessor ) < leftFence; i += 1 ) ;
leftOutliers = { begin: 0, end: ( i - 1 ), count: i, fence: value( sortedData[ i ], accessor ) };
// Compute right outliers, if any.
for ( i = fns.size - 1; value( sortedData[ i ], accessor ) > rightFence; i -= 1 ) ;
rightOutliers = { begin: ( i + 1 ), end: ( fns.size - 1 ), count: ( fns.size - i - 1 ), fence: value( sortedData[ i ], accessor ) };
// Add left and/or right outliers to `rs`.
if ( leftOutliers.count ) fns.leftOutliers = leftOutliers;
if ( rightOutliers.count ) fns.rightOutliers = rightOutliers;
}