# Definition:Mode

## 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 $M$.