Commonest

Every element tied for the most frequently occurring in the collection.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageCommonest✓↗

Commonest(collection)every element tied for the highest frequency, in the order first encountered.

Commonest(collection, n)the $n$ commonest elements, ties broken by first appearance, listed in order of first appearance.

Typed signatures

Type	Package	Applies
(indexed_collection<T>, integer?) -> list<T> where T	combinatorics	always

Domain: Collections

Details

• Wolfram's answer to a tied Mode: where Mode picks one, Commonest returns every value tied for the highest frequency.
• With a unique mode, $Commonest(c) = \{Mode(c)\}$: a single-element list.
• Every returned value occurs exactly as many times as the highest frequency in the collection. See Count.

Examples

Basic #

live ↗

In$\mathrm{Commonest}(\bigl\lbrack1, 1, 2, 2, 3\bigr\rbrack)$Out$\bigl\lbrack1, 2\bigr\rbrack$

With a unique mode, Commonest returns a single-element list

live ↗

In$\mathrm{Commonest}(\bigl\lbrack1, 2, 2, 3\bigr\rbrack)$Out$\bigl\lbrack2\bigr\rbrack$

Every element tied for most frequent, symbols and numbers alike

live ↗

In$\mathrm{Commonest}(\bigl\lbrack b, a, c, 2, a, b, 1, 2\bigr\rbrack)$Out$\bigl\lbrack b, a, 2\bigr\rbrack$

A single most-frequent element still comes back in a list

live ↗

In$\mathrm{Commonest}(\bigl\lbrack1, 2, 2, 3, 3, 3, 4\bigr\rbrack)$Out$\bigl\lbrack3\bigr\rbrack$

live ↗

In$\mathrm{Commonest}(\bigl\lbrack b, a, c, 2, a, b, 1, 2\bigr\rbrack, 4)$Out$\bigl\lbrack b, a, c, 2\bigr\rbrack$

live ↗

In$\mathrm{Commonest}(\bigl\lbrack b, a, c, 2, a, b, 1, 2\bigr\rbrack, \mathrm{UpTo}(6))$Out$\bigl\lbrack b, a, c, 2, 1\bigr\rbrack$

Scope #

All distinct: all tie

live ↗

In$\mathrm{Commonest}(\bigl\lbrack1, 2, 3\bigr\rbrack)$Out$\bigl\lbrack1, 2, 3\bigr\rbrack$

The $n$ commonest, ties broken by first appearance

live ↗

In$\mathrm{Commonest}(\bigl\lbrack1, 2, 2, 3, 3, 3, 4\bigr\rbrack, 2)$Out$\bigl\lbrack2, 3\bigr\rbrack$

Numeric input still picks the most frequent value, 3

live ↗

In$\mathrm{Commonest}(N(\bigl\lbrack1, 2, 2, 3, 3, 3, 4\bigr\rbrack))$Out$\bigl\lbrack3.0\bigr\rbrack$

Higher-precision numeric input gives the same mode

live ↗

In$\mathrm{Commonest}(N(\bigl\lbrack1, 2, 2, 3, 3, 3, 4\bigr\rbrack, 30))$Out$\bigl\lbrack3.0\bigr\rbrack$

live ↗

In$\mathrm{Commonest}(\mathrm{data})$Out$\mathrm{Commonest}(\mathrm{data})$

live ↗

In$\mathrm{Commonest}(\bigl\lbrack a, e, \sin(y), e, a, 7\bigr\rbrack)$Out$\bigl\lbrack a, e\bigr\rbrack$

Applications #

live ↗

In$\mathrm{Commonest}(\mathrm{heights})$Out$\mathrm{Commonest}(\mathrm{heights})$

Properties #

With a unique mode, $Commonest(c) = \{Mode(c)\}$. See Mode

live ↗

In$\mathrm{First}(\mathrm{Commonest}(\bigl\lbrack1, 2, 2, 3\bigr\rbrack))$Out$2$

Without a tie, the single commonest element is the Mode

live ↗

In$\mathrm{First}(\mathrm{Commonest}(\bigl\lbrack1, 2, 2, 3, 3, 3, 4\bigr\rbrack))=\mathrm{Mode}(\bigl\lbrack1, 2, 2, 3, 3, 3, 4\bigr\rbrack)$Out$\mathrm{True}$

A frequency tie between $4$ and $1$ is broken by first appearance in the list.

live ↗

In$\mathrm{Commonest}(\bigl\lbrack4, 1, 1, 4\bigr\rbrack, 1)$Out$\bigl\lbrack4\bigr\rbrack$

About

Examples	16
Checked against	Wolfram Language 16 agree
Crosswalk	Wolfram Language

See also: Mode, Mean, Median