Topics: Statistics


Let be observations of a random variable and let .

A quantile to the is the value c that satisfies the following two conditions:

…where denotes the cardinality of .


A is basically the value up to which the of the variable’s mass is accumulated.

See, for instance, the location of the quartiles () of a normal distribution:

(courtesy of Wikimedia Commons)

Particular Cases

  • Decile: if
  • Quartile: if
  • Percentile: if

Notice that the second quartile is the median.