terciles

A tercile is a value or point that divides a dataset or probability distribution into three equal parts. In statistics, data can be partitioned into three groups of roughly equal size: the lower tercile, the middle tercile, and the upper tercile. The cutpoints correspond to the 1/3 and 2/3 quantiles, i.e., the 33.333...th and 66.666...th percentiles.

For a random variable X with distribution function F, the lower tercile t1 satisfies F(t1) = 1/3 and the upper tercile t2 satisfies F(t2) = 2/3. In continuous distributions these cutpoints are unique; in discrete distributions they may fall between observed values or coincide with them, depending on the quantile method used (often involving interpolation).

In practice, terciles are estimated from samples by computing the corresponding sample quantiles. For an ordered sample x(1) ≤ ... ≤ x(n), the lower tercile is near the 1/3 position and the upper tercile near the 2/3 position, with different software using various interpolation rules.

Uses and notes: terciles are a simple way to summarize a distribution and to create three-category groups for comparison or risk classification without assuming a parametric form. They are related to quartiles and quintiles as parts of the broader family of quantile-based descriptive statistics.

See also: quartiles, quintiles, percentiles, quantiles.