# BinCounts

BinCounts[data]

counts the number of elements of data whose values lie in successive integer bins.

BinCounts[data,binspec]

counts the number of elements of data whose values lie in successive bins specified by binspec.

# Details

• BinCounts 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, …},…} »
• BinCounts[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].
• BinCounts[data] is equivalent to BinCounts[data,1].
• In BinCounts[data,{xmin,xmax,dx}], elements are counted in bin i when their values satisfy .
• BinCounts[data,{xmin,xmax}] is equivalent to BinCounts[data,{xmin,xmax,1}].
• In BinCounts[data,{{b1,b2,}}], elements are counted in bin i when their values satisfy .
• In the form BinCounts[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 BinCounts.
• If data consists of length-n sublists, then n bin specifications must be given, and BinCounts[data,] yields an array of depth n.
• 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) »

# Examples

open allclose all

## Basic Examples(3)

Count the number of elements in bins of a specified width:

Count the number of elements in bins of width 1 from 0 to 10:

Count the number of elements in a sequence of ranges:

## Scope(11)

### Basic Uses(8)

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

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

Count multidimensional data in ranges:

Count data in any dimension:

Count binned data, ignoring values that are not real:

Count binned data of any precision:

SparseArray data can be used just like dense arrays:

Count the values of data in 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:

## Applications(1)

Visualize the density of two-dimensional data in bins:

## Properties & Relations(1)

The results from BinCounts are equivalent to the lengths of BinLists:

For 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), BinCounts, Wolfram Language function, https://reference.wolfram.com/language/ref/BinCounts.html (updated 2024).

#### Text

Wolfram Research (2007), BinCounts, Wolfram Language function, https://reference.wolfram.com/language/ref/BinCounts.html (updated 2024).

#### CMS

Wolfram Language. 2007. "BinCounts." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/BinCounts.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_bincounts, author="Wolfram Research", title="{BinCounts}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/BinCounts.html}", note=[Accessed: 12-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_bincounts, organization={Wolfram Research}, title={BinCounts}, year={2024}, url={https://reference.wolfram.com/language/ref/BinCounts.html}, note=[Accessed: 12-September-2024 ]}