kvartil

Kvartil is a statistical concept that divides a data set into four equal parts when the data are ordered from smallest to largest. The three cut points at 25%, 50%, and 75% are called the first, second, and third quartiles, commonly denoted Q1, Q2, and Q3. In percent terms, Q1 corresponds to the 25th percentile, Q2 to the 50th percentile (the median), and Q3 to the 75th percentile. The spread of the middle half of the data is measured by the interquartile range, IQR = Q3 − Q1.

There are practical differences in calculating quartiles, especially for small samples. A standard approach is to take Q2 as the median of the data, and then Q1 and Q3 as the medians of the lower and upper halves of the data, respectively. Other conventions interpolate between data points or include the median in the halves. Because of these differences, quartile values can vary slightly depending on the method used.

Quartiles are widely used for describing distributions and for graphical representations such as box plots. They help reveal skewness and compare distributions across data sets. The IQR is also used to identify outliers, with observations below Q1 − 1.5·IQR or above Q3 + 1.5·IQR often considered unusual.

Example: for the ordered data set 2, 5, 7, 9, 10, 12, 14, 18, the median Q2 is (9+10)/2 = 9.5. The lower half 2,5,7,9 yields Q1 = (5+7)/2 = 6, and the upper half 10,12,14,18 yields Q3 = (12+14)/2 = 13. Different calculation methods may produce nearby values.