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CountsBy[{e1,e2,…},f]

gives an association whose keys are the distinct values of the f[ei], and whose values give the number of times these f[ei] values appear.

CountsBy[f]

represents an operator form of CountsBy that can be applied to an expression.

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CountsBy

CountsBy[{e1,e2,…},f]

gives an association whose keys are the distinct values of the f[ei], and whose values give the number of times these f[ei] values appear.

CountsBy[f]

represents an operator form of CountsBy that can be applied to an expression.

Details

  • CountsBy[{e1,e2,…},f] gives an association whose keys f[ei] are in the order in which the corresponding ei first appear. »
  • CountsBy[f][expr] is equivalent to CountsBy[expr,f].

Examples

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Basic Examples  (2)

Count the even and odd elements of a list:

Wolfram Language code: CountsBy[{1, 2, 3, 2, 1, 1}, EvenQ]

Count the prime and composite numbers in a list:

Wolfram Language code: CountsBy[Range[1000], PrimeQ]

Use the operator form of CountsBy:

Wolfram Language code: CountsBy[PrimeQ][Range[1000]]

Scope  (1)

Count elements have the same absolute value:

Wolfram Language code: CountsBy[{-1, 0, 1, 0, -1, 1}, Abs]

Count using the operator form:

Wolfram Language code: {-1, 0, 1, 0, -1, 1}//CountsBy[Abs]

Properties & Relations  (3)

Elements in the result appear in the order in which values of f[ei] appear in the list:

Wolfram Language code: numbers = {0, 1, -1, I, -I, 1 + I, 1 - I, -1 + I, -1 + I} CountsBy[numbers, Abs]

Reverse the elements of the list, and the order of counts is reversed:

Wolfram Language code: CountsBy[Reverse[numbers], Abs]

Move zero to the end of the list, and yet another order of counts is generated:

Wolfram Language code: CountsBy[RotateLeft[numbers], Abs]

CountsBy[list,f] is effectively Counts[Map[f,list]]:

Wolfram Language code: list = RandomInteger[{-1, 1}, 100]; CountsBy[list, Abs] === Counts[Map[Abs, list]]

In particular, CountsBy[list,Identity] is equivalent to Counts[list]:

Wolfram Language code: CountsBy[list, Identity] === Counts[list]

CountsBy[expr,f] is equivalent to GroupBy[expr,f,Length]:

Wolfram Language code: CountsBy[{{a, b}, {b, c}, {a, d}}, First] == GroupBy[{{a, b}, {b, c}, {a, d}}, First, Length]
Wolfram Research (2014), CountsBy, Wolfram Language function, https://reference.wolfram.com/language/ref/CountsBy.html.

Text

Wolfram Research (2014), CountsBy, Wolfram Language function, https://reference.wolfram.com/language/ref/CountsBy.html.

CMS

Wolfram Language. 2014. "CountsBy." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CountsBy.html.

APA

Wolfram Language. (2014). CountsBy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CountsBy.html

BibTeX

@misc{reference.wolfram_2026_countsby, author="Wolfram Research", title="{CountsBy}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/CountsBy.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_countsby, organization={Wolfram Research}, title={CountsBy}, year={2014}, url={https://reference.wolfram.com/language/ref/CountsBy.html}, note=[Accessed: 12-June-2026]}