The First Quartile ($Q_1$) and Third Quartile ($Q_3$) represent specific quantiles within a cumulative distribution function that partition the data set into four equal parts, each containing 25% of the observations. $Q_1$ corresponds to the value below which 25% of the population falls, while $Q_3$ denotes the threshold encompassing the lower 75%, together defining the interquartile range as a robust measure of statistical dispersion. This concept operates strictly within inferential and descriptive statistics, serving as a fundamental mechanism for characterizing data distribution shape without reliance on extreme values in mathematical modeling.
Prerequisite chain context: requires Descriptive Statistics in Data Science.