Topics: Statistics
(definition)
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 .
Meaning
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.