puolijohdemedian

Puolijohdemedian is a term found in some Finnish statistical writings to describe a median calculated within one half of an ordered data set. The concept is used to summarize central tendency separately for the lower and upper portions of the data, which can help assess symmetry or differences between halves.

To compute a puolijohdemedian, you first sort the data from smallest to largest. Then you split the data into two halves. The lower-half median is the median of the first half, and the upper-half median is the median of the second half. If a half contains an even number of observations, its median is the average of the two central values; if it contains an odd number, the central value of that half is used. There are variations in how the split is performed when the overall sample size is odd, which can affect the exact values, so clarifying the convention is important.

Relation to quartiles: the lower-half median under the common convention often coincides with the first quartile (Q1), and the upper-half median with the third quartile (Q3). However, different data-analysis traditions may treat the division of halves with slight differences, so terminology and exact calculation can vary.

Usage and interpretation: puolijohdemedian is primarily a descriptive statistic used in exploratory data analysis to examine central tendency within each half of the data. It provides a sense of asymmetry and how the halves differ, complementing the overall median and the quartiles. It is not a standard inferential estimator on its own, but it can support robust summaries and visualizations such as split-box plots.

Notes: The exact terminology and conventions for puolijohdemedian are not universally fixed; some Finnish sources may use related terms or alternative splitting rules.