Quantiles are cut points that divide a probability distribution into contiguous intervals with equal probabilities. They are used to understand the distribution of data by segmenting it into equal-sized, ordered subgroups.
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Quantiles include quartiles, deciles, and percentiles depending on how many intervals the data is divided into.
The median is a special case of a quantile, specifically the 50th percentile or the second quartile.
To calculate quantiles, data must first be ordered from smallest to largest.
Quantiles can help identify outliers and understand the spread and skewness of data distributions.
In statistical software, functions for finding quantiles often require you to specify which quantile you want (e.g., 25th percentile for the first quartile).
Review Questions
What is a quantile and how does it differ from a percentile?
How would you explain the process of calculating a quantile in an ordered dataset?
Why are quantiles important in understanding data distributions?
Related terms
Percentile: A measure indicating the value below which a given percentage of observations fall.
Quartile: A type of quantile that divides data into four equal parts.