kvartilen

Kvartilen, or quartile in English, is a statistical measure that divides a dataset into four equal parts. The three cut points are the first, second, and third quartiles, usually denoted Q1, Q2, and Q3. The second quartile Q2 is the median, representing the 50th percentile; Q1 and Q3 correspond to the 25th and 75th percentiles, respectively.

Calculation is based on ordered data. Q2 is the median of the data. Q1 is the median of the lower half, and Q3 is the median of the upper half. Different conventions exist for how to handle the median and how to split the data, especially for small samples; some definitions are inclusive, others exclusive, and interpolation can be used for non-integer positions.

The interquartile range (IQR) is Q3 minus Q1 and measures the spread of the middle 50% of the data. Box plots visualize quartiles, highlighting the IQR and potential outliers. Outliers are commonly defined as observations more than 1.5 times the IQR below Q1 or above Q3.

Uses include providing a quick, robust summary of a distribution, aiding in the assessment of skewness, and supporting non-parametric analyses. For example, a dataset such as 3, 7, 8, 12, 13, 14, 18, 21, 22 yields Q1 around 7.5, Q2 13, Q3 around 19.5, and an IQR of about 12.

In Swedish statistical terminology, kvartilen denotes the quartile, with kvartiler as the plural. The definite form kvartilen refers to a specific quartile (for example, the first kvartil or the median).