Glossary
Quantile
A value that divides an ordered dataset into equal-sized subsets. The 0.5 quantile is the median; the 0.25 and 0.75 quantiles are the first and third quartiles. More generally, the τ-th quantile (0 < τ < 1) is the value below which a fraction τ of the data lies. Quantiles are ...
Definition
A value that divides an ordered dataset into equal-sized subsets. The 0.5 quantile is the median; the 0.25 and 0.75 quantiles are the first and third quartiles. More generally, the τ-th quantile (0 < τ < 1) is the value below which a fraction τ of the data lies. Quantiles are robust to outliers and form the basis of quantile regression.
Why It Matters
Quantiles provide a complete picture of a distribution's shape, not just its centre. In income analysis, for example, the median and 90th percentile tell very different stories about economic well-being. Quantiles are also the foundation of quantile regression, which models how covariates affect different parts of the response distribution — not just the conditional mean.
Example
In a study of household incomes, the 0.10 quantile (10th percentile) is $18,000, the median (0.50 quantile) is $52,000, and the 0.90 quantile is $145,000. These three values summarise the lower, middle, and upper portions of the income distribution far more informatively than the mean alone.
Related Terms
Software Notes
- SPSS: Analyze > Descriptive Statistics > Explore; or use
Frequencieswith percentiles - R:
quantile(x, probs = c(0.10, 0.50, 0.90)) - Stata:
summarize variable, detailorqregfor quantile regression