Quantiles

Population Quantiles

For any $q$, with $0<q<1$, the population quantile (tau) ${\tau }_{X,q}$ of a continuous variable $X$ is the value for which:

$P(X\le {\tau }_{X,q})=F_X({\tau }_{X,q})=q$ Population median (special case):

$P(X\le {\tau }_{X,0.5})=F_X({\tau }_{X,0.5})=0.5$