Quantiles are points taken at regular intervals from the
cumulative distribution function of a
random variable. Dividing ordered data into q essentially equal-sized data subsets is the motivation for q-quantiles; the quantiles are the data values marking the boundaries between consecutive subsets. Put another way, the kth q-quantile is the value x such that the probability that a random variable will be less than x is at most k/q and the probability that a random variable will be less than or equal to x is at least k/q. There are q − 1 quantiles, with k an integer satisfying 0 < k < q.
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The quantile (this term was first used by Kendall, 1940) of a distribution of values is a number xp such that a proportion p of the population values are less than or equal to xp. For example, the .25 quantile (also referred to as the 25th
percentile or lower
quartile ) of a variable is a value (xp) such that 25% (p) of the values of the variable fall below that value.
Similarly, the .75 quantile (also referred to as the 75th percentile or upper quartile) is a value such that 75% of the values of the variable fall below that value and is calculated accordingly.
See also,
Quantile-Quantile Plots
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