Mode

The most frequently occurring element of the collection.

WikipediaMode (statistics)↗MathWorldMode↗WikidataQ188224↗Britannicatopic/mode-mathematics↗

Mode(collection)the most frequently occurring element.

Typed signatures

Type	Package	Applies
((collection<nothing | number> | number)+) -> nan | real | signed_infinity	combinatoricsreplaces compute-engine	always
((collection<nothing | number> | number)+) -> nan | real | signed_infinity	compute-engine	always

Domain: Collections

Details

• The mode occurs exactly as many times as the highest frequency in the collection: $Count(c, Mode(c))$ gives that frequency. See Count.
• When several elements share the highest frequency, Mode returns just one. See Commonest for every tied value.
• See Mean and Median for other measures of central tendency.

Examples

Basic #

live ↗

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

live ↗

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

Scope #

Exact rationals

live ↗

In$\mathrm{Mode}(\bigl\lbrack\frac{1}{2}, 1, \frac{1}{2}\bigr\rbrack)$Out$\frac{1}{2}$

Symbols and numbers mixed, three-way tie: the first to appear wins; Commonest lists all three, $b$, $a$, $2$, as Wolfram's does

live ↗

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

Properties #

The mode occurs exactly as many times as the highest frequency in the collection. See Count

live ↗

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

Possible issues #

With a tie for most frequent, Mode returns just one; see Commonest for every tied value

live ↗

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

Empty data has no mode; compute-engine returns $NaN$

live ↗

In$\mathrm{Mode}(\bigl\lbrack\bigr\rbrack)$Out$\operatorname{NaN}$

About

Examples	7
Checked against	Wolfram Language 6 agree1 differ
Crosswalk	WikipediaMathWorldWikidataBritannica

See also: Mean, Median, Commonest