Quantile

A quantile is a cutoff point that divides an ordered dataset into equal-sized groups. Quantiles help describe the distribution of values by indicating where data fall relative to the entire dataset. The quantiles that analysts use most frequently include quartiles (4 equal groups), deciles (10 groups), and percentiles (100 groups).

Each quantile corresponds to a proportion of the dataset, ranging from 0 to 1. For example:

• The 0.25 quantile (25th percentile) marks the value below which 25% of the data fall.
• The 0.5 quantile (50th percentile) is the median.
• The 0.75 quantile (75th percentile) marks the point below which 75% of the data fall.

This proportional format is commonly used in mathematical notation and statistical software. However, in everyday usage, quantiles are often expressed as percentiles (e.g., “the 90th percentile”) or quartiles (e.g., Q1, Q2, Q3).

Quantiles are useful for summarizing distributions, identifying relative rankings, and comparing values across populations. Analysts frequently use them in statistics, data science, and reporting to describe spread, detect outliers, or compare individual values to a broader group.

For example, in a dataset of household incomes, the 0.25 quantile (also called the lower quartile) is $35,000. This means that 25% of the households earn less than $35,000, and 75% earn more.