Kvartiiliväli

Kvartiiliväli, often called the interquartile range (IQR) in English, is a measure of statistical dispersion that describes the spread of the middle half of a data set. It is defined as the difference between the third quartile (Q3, the 75th percentile) and the first quartile (Q1, the 25th percentile): IQR = Q3 − Q1. By focusing on the central portion of the data, the kvartiiliväli provides a summary of variability that is less influenced by extreme values than the full range.

Calculation can be done exactly or approximately, depending on the data size and the method used to estimate quartiles. In a sorted data set, Q1 is often taken as the median of the lower half and Q3 as the median of the upper half. In practice, many software packages implement a variety of quartile definitions, so the resulting IQR may vary slightly with the method chosen.

Interpretation and uses: a larger kvartiiliväli indicates greater variability in the middle 50% of the data, while a smaller value suggests the middle portion is more tightly clustered around the median. The IQR is robust to outliers and is commonly visualized in box plots, where it forms the height of the box. It also enters outlier detection, with commonly used fences at Q1 − 1.5×IQR and Q3 + 1.5×IQR.

Limitations: the kvartiiliväli does not describe the distribution’s shape or tails beyond the central 50%, and its exact numerical value depends on the quartile definition used. Nevertheless, it remains a fundamental, robust measure of spread in descriptive statistics and comparative data analysis.