# BinLists

BinLists[data]

gives lists of the elements of data whose values lie in successive integer bins.

BinLists[data,binspec]

gives lists of the elements of data whose values lie in successive bins specified by binspec.

BinLists[datainds,]

gives the lists of the labels inds specified by the binning of data.

# Details

• BinLists drops elements whose values do not correspond to real numbers.
• The following bin-width specifications binspec can be given:
•  dx bins of width dx » {xmin,xmax,dx} bins of width dx from xmin to xmax » {{b1,b2,…}} the intervals [b1,b2), [b2,b3), … » xbins,ybins,… bin specifications for multivariate data understood as {{x1,y1,…},{x2,y2, …},…} »
• BinLists[data,dx] takes the bin boundaries to be integer multiples of dx, with the first bin starting at Ceiling[Min[data]-dx,dx] and the last bin ending at Floor[Max[data]+dx,dx].
• BinLists[data] is equivalent to BinLists[data,1].
• In BinLists[data,{xmin,xmax,dx}], elements are placed in bin i when their values satisfy .
• BinLists[data,{xmin,xmax}] is equivalent to BinLists[data,{xmin,xmax,1}].
• In BinLists[data,{{b1,b2,}}], elements are put in bin i when their values satisfy .
• In the form BinLists[data,{{b1,b2,}}], the bi at each end can be and .
• If the bi do not form an increasing sequence, they are automatically sorted by BinLists.
• If data consists of length-n sublists, then n bin specifications must be given, and BinLists[data,] yields an array of lists of depth n.
• Within each bin, elements appear in the same order as in the original data.
• The data can have the following forms and interpretations:
•  {x1,x2,…} list of real numbers or quantities » {{x1,y1,…},{x2,y2,…},…} list of vectors of the same dimension » SparseArray an array equivalent to Normal[data] » QuantityArray array of column-compatible quantities » TimeSeries, TemporalData,… vector or array of values (the time stamps ignored) »
• Labels inds for the input elements xi can be given in the following formats: »
•  {x1,x2,…} use the xi themselves (no labels by default) {x1,x2,…}Automatic use integer labels {x1,x2,…}{v1,v2,…} a rule between all the elements and all the labels {x1v1,x2v2,…} a list of rules between the element xi and its label vi

# Examples

open allclose all

## Basic Examples(3)

List elements in bins of a specified width:

Make lists of elements in bins of width 1 from 0 to 10:

List elements in a sequence of ranges:

## Scope(12)

### Basic Uses(8)

List squares mod 3 and 5 in two-dimensional unit bins:

List random pairs in bins of width 0.25 in both dimensions:

List multidimensional data in ranges:

Bin data in any dimension:

Bin data, ignoring values that are not real:

Bin data of any precision:

SparseArray data can be used just like dense arrays:

Bin data from a time series:

The time stamps are ignored:

### Data with Quantities(3)

Bin quantity data:

Automatic bins:

Specify bin width:

Bins of fixed width, minimum and maximum:

Specify bin intervals:

Bin mixed-type data:

The units are compatible for each dimension:

Specify bin width for each dimension:

QuantityArray can be used just like arrays:

Automatic bins:

Specify bin width in compatible units:

### Data with Labels(1)

Bin data with output as an array of labels:

Bin data with default integer labels:

## Applications(1)

Visualize two-dimensional data in bins:

## Properties & Relations(1)

The length of BinLists is equivalent to the results from BinCounts:

For a list of vectors:

## Possible Issues(4)

Binning intervals are closed on the left:

For data involving quantities, the bin specification must be given in compatible units:

Matrix data must have unit-compatible columns:

The bins obtained using the specification {min,max,dx} may not include all data points:

Specify the min and max so all data points are included in the bin covering:

Alternatively, use the width-only bin specification dx:

Wolfram Research (2007), BinLists, Wolfram Language function, https://reference.wolfram.com/language/ref/BinLists.html (updated 2023).

#### Text

Wolfram Research (2007), BinLists, Wolfram Language function, https://reference.wolfram.com/language/ref/BinLists.html (updated 2023).

#### CMS

Wolfram Language. 2007. "BinLists." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/BinLists.html.

#### APA

Wolfram Language. (2007). BinLists. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BinLists.html

#### BibTeX

@misc{reference.wolfram_2024_binlists, author="Wolfram Research", title="{BinLists}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/BinLists.html}", note=[Accessed: 20-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_binlists, organization={Wolfram Research}, title={BinLists}, year={2023}, url={https://reference.wolfram.com/language/ref/BinLists.html}, note=[Accessed: 20-May-2024 ]}