For numerical data ranked in ascending order, the quartiles are values derived from the data which divide the data into four equal parts. If there are n observations, the first quartile (or lower quartile) Q₁ is the $\frac{1}{4}(n+1)$-th, the second quartile (which is the median) Q₂ is the $\frac{1}{2}(n+1)$-th, and the third quartile (or upper quartile) Q₃ is the $\frac{3}{4}(n+1)$-th in ascending order. When $\frac{1}{4}(n+1)$ is not a whole number, it is sometimes thought necessary to take the (weighted) average of two observations, as is done for the median. However, unless n is very small, an observation that is nearest will normally suffice. For example, for the sample 15, 37, 43, 47, 54, 55, 57, 64, 76, 98, we may take Q₁=43, Q₂=54.5, and Q₃=64.

For a random variable, the quartiles are the quantiles x_0.25, x_0.5, and x_0.75; that is, the 25th, 50th, and 75th percentiles.