# Definition:Mode

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## Definition

Let $S$ be a set of quantitative data.

The **mode** of $S$ is the element of $S$ which occurs most often in $S$.

If there is more than one such element of $S$ which occurs equally most often, it is then understood that each of these is a **mode**.

If there is no element of $S$ which occurs more often (in the extreme case, all elements are equal) then $S$ has **no mode**

### Continuous Random Variable

Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $X$ have probability density function $f_X$.

We call $M$ a **mode** of $X$ if $f_X$ attains its (global) maximum at $M$.

## Also see

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**mode**

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