kwartiel

A kwartiel (Dutch for quartile) is a statistical value that divides a finite data set into four equal parts. In practice, it identifies three cut points that separate the data into quarters, with Q1 at the 25th percentile, Q2 at the 50th percentile (the median), and Q3 at the 75th percentile. The term is used in several languages with similar concepts, and in Dutch statistical writing it is commonly referred to as a kwartiel.

There are multiple conventions for calculating kwartielen, especially for small data sets. A percentile-based approach defines Q1, Q2, and Q3 as the 25th, 50th, and 75th percentiles, possibly using interpolation between data points. A common alternative, sometimes called Tukey’s hinges, defines Q1 as the median of the lower half of the data and Q3 as the median of the upper half, with the overall median serving as Q2. Different methods can yield slightly different values, particularly for discrete or small samples. Overall, the quartiles are robust to extreme values and are used to summarize distribution shape.

The interquartile range (IQR), calculated as Q3 minus Q1, measures the spread of the middle half of the data. Quartiles underpin box plots and are frequently used to detect skewness and outliers, compare distributions, and accompany descriptive statistics in reports.

Example: for the ordered data set 1, 3, 5, 7, 9, 11, 13, 15 (n = 8), Q1 = 4, Q2 = 8, Q3 = 12 (depending on method), giving an IQR of 8. This illustrates how quartiles summarize central tendency and dispersion.

---