# BinCounts

BinCounts[{x1,x2,}]

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

BinCounts[{x1,x2,},dx]

counts the number of elements xi whose values lie in successive bins of width dx.

BinCounts[{x1,x2,},{xmin,xmax,dx}]

counts the number of xi in successive bins of width dx from xmin to xmax.

BinCounts[{x1,x2,},{{b1,b2,}}]

counts the number of xi in the intervals [b1,b2), [b2,b3), .

BinCounts[{{x1,y1,},{x2,y2,},},xbins,ybins,]

gives an array of counts where the first index corresponds to x bins, the second to y, and so on.

# Details • BinCounts drops elements whose values do not correspond to real numbers.
• 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].
• BinCounts[data,{xmin,xmax}] is equivalent to BinCounts[data,{xmin,xmax,1}].
• In BinCounts[data,{xmin,xmax,dx}], 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.
• In BinCounts[data,{{b1,b2,}}], elements are counted in bin i when their values satisfy .
• If data consists of length-n sublists, then n bin specifications must be given, and BinCounts[data,] yields an array of depth n.
• BinCounts works with SparseArray objects.

# Examples

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## Basic Examples(3)

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

Count the number of elements in a sequence of ranges:

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

## Scope(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:

Count the values of data in a time series:

The time stamps are ignored:

Count data in a SparseArray:

## 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:

## Possible Issues(1)

Binning intervals are closed on the left: