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Calculating the Quantiles

There are several methods for calculating the quantiles:

Let n by the number of nonmissing values for a variable, and let represent the ordered values of the variable such that is the smallest value, etc. For the Tth N-quantile between 0 and N, let . Then define as the integer part of or and as the fractional part.

• Weighted average at

• Weighted average at - generally used for a sample

• Empirical distribution function

• Empirical distribution function with averaging

• Observation numbered closest to np

In percentiles, N = 100; in quartiles, N = 4.

See also:

• Summary statistics
• Descriptive statistics
• Percentile
• Quartile

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Topics: Quantile Quantiles Variable Values Data Function Random...

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Quantilepercentile, quartile Quantiles are essentially points taken at regular vertical 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;