Kvartetille

Kvartetille is a statistical term used to describe the boundaries that partition a data set into four equal parts. It is closely related to quartiles and is used in descriptive statistics to summarize the distribution of a variable. The quartetile set typically includes Q1, Q2, and Q3 as the primary cutpoints, with the fourth quartile comprising the top 25% of observations.

Definition and interpretation: Q1 is the 25th percentile, Q2 is the median (the 50th percentile), and Q3 is the 75th percentile. The data are thus divided into four groups of roughly equal size. The fourth quartile refers to the portion of data above Q3, representing the highest values in the distribution.

Calculation: There are several conventions for computing quartiles in a finite data set. A common method orders the data and defines Q1 as the median of the lower half, Q2 as the overall median, and Q3 as the median of the upper half. Another approach uses linear interpolation: Qp = x_(p*(n+1)/4) for p = 1, 2, 3. Different software packages may yield slightly different results depending on the method chosen.

Example: For the data set 1, 2, 3, 4, 5, 6, 7, 8, using the lower-half method gives Q1 = 2.5, Q2 = 4.5, and Q3 = 6.5, with the top 25% forming the fourth quartile above Q3.

Applications: Quartile boundaries are used in box plots, summary statistics, and in identifying skewness and potential outliers.

See also: Quartile, Percentile, Decile.