Definition: Mode

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Measures of central tendency ▷ Mode

Definition: The mode of a sample or random variable is the value which occurs most often or with largest probability among all its values.

1) Let $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$ be a sample from a random variable $X$. Then, the mode of $x$ is the value which occurs most often in the list $x_1, \ldots, x_n$.

2) Let $X$ be a random variable with probability mass function or probability density function $f_X(x)$. Then, the mode of $X$ is the the value which maximizes the PMF or PDF:

\[\label{eq:mode-rvar} \mathrm{mode}(X) = \operatorname*{arg\,max}_x f_X(x) \; .\]

 

Sources:

• Wikipedia (2020): "Mode (statistics)"; in: Wikipedia, the free encyclopedia, retrieved on 2020-10-15; URL: https://en.wikipedia.org/wiki/Mode_(statistics).

Metadata: ID: D102 | shortcut: mode | author: JoramSoch | date: 2020-10-15, 11:10.