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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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Basic Uses  
Data with Quantities  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
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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:
  • dxbins 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 -Infinity and +Infinity.
  • 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 »
    SparseArrayan array equivalent to Normal[data] »
    QuantityArrayarray of column-compatible quantities »
    TimeSeries, TemporalData,…vector or array of values (the time stamps ignored) »

Examples

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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_2025_bincounts, author="Wolfram Research", title="{BinCounts}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/BinCounts.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_bincounts, organization={Wolfram Research}, title={BinCounts}, year={2024}, url={https://reference.wolfram.com/language/ref/BinCounts.html}, note=[Accessed: 01-December-2025]}