In statistics, quartiles are a type of quantiles which divide the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic. The three quartiles, resulting in four data divisions, are as follows:

Along with the minimum and maximum of the data (which are also quartiles), the three quartiles described above provide a five-number summary of the data. This summary is important in statistics because it provides information about both the center and the spread of the data. Knowing the lower and upper quartile provides information on how big the spread is and if the dataset is skewed toward one side. Since quartiles divide the number of data points evenly, the range is generally not the same between adjacent quartiles (i.e. usually (Q₃ - Q₂) ≠ (Q₂ - Q₁)). Interquartile range (IQR) is defined as the difference between the 75th and 25th percentiles or Q₃ - Q₁. While the maximum and minimum also show the spread of the data, the upper and lower quartiles can provide more detailed information on the location of specific data points, the presence of outliers in the data, and the difference in spread between the middle 50% of the data and the outer data points.

For discrete distributions, there is no universal agreement on selecting the quartile values.

This rule is employed by the TI-83 calculator boxplot and "1-Var Stats" functions.

The values found by this method are also known as "Tukey's hinges"; see also midhinge.

If we have an ordered dataset ${\displaystyle x_{1},x_{2},...,x_{n}}$, then we can interpolate between data points to find the ${\displaystyle p}$th empirical quantile if ${\displaystyle x_{i}}$ is in the ${\displaystyle i/(n+1)}$ quantile. If we denote the integer part of a number ${\displaystyle a}$ by ${\displaystyle \lfloor a\rfloor }$, then the empirical quantile function is given by,

${\displaystyle q(p/4)=x_{k}+\alpha (x_{k+1}-x_{k})}$,

${\displaystyle x_{k}}$ is the last data point in quartile p, and ${\displaystyle x_{k+1}}$ is the first data point in quartile p+1.