deciles

Deciles are statistical cutpoints that partition a dataset into ten equal-sized groups. They correspond to the 10th, 20th, …, 90th percentiles of a distribution, and are often denoted as D1 through D9. In population terms, Dk is the value below which k×10 percent of observations fall. As a set, the deciles summarize the distribution by indicating its spread and where observations concentrate.

Calculation and estimation are based on order statistics. In a sample, deciles are the quantiles at probabilities p = 0.1, 0.2, …, 0.9. When data are sorted, practitioners may use different methods to handle non-integer ranks, such as linear interpolation between surrounding data points or the nearest-rank approach, which selects the value at rank ceil(n×p). As a result, different software packages may yield slightly different decile values for the same dataset.

Interpretation: Deciles help describe distributional shape, identify skew, and compare groups. D1 and D9 bound the central 80% of observations, while D5 typically coincides with the median (the 50th percentile) in many conventions. In symmetric distributions, deciles align with central tendency measures; in skewed distributions they reveal asymmetry.

Applications: Deciles are used in economics to analyze income or wealth distribution, in education to assess test-score dispersion, and in various fields to monitor performance or resource allocation. They are related to, but distinct from, quintiles, quartiles, and percentiles, representing fixed 10% increments of the distribution.