Kohdemedian

Kohdemedian is a statistical measure of central tendency used to summarize data with respect to a user-defined target subset. It generalizes the conventional median by restricting the data considered to observations whose associated target attribute falls within a specified set, thereby focusing the summary on a particular subpopulation or condition.

Definition and computation: Let the data consist of pairs (t_i, x_i) for i = 1,...,n, and let T be the target subset of possible t-values. Form the subset S = { x_i : t_i ∈ T }. If S is nonempty, the kohdemedian is the median of S. If S contains an even number of elements, the usual convention for a median of two middle values applies. If S is empty, the kohdemedian is undefined or may be defined by a predefined fallback value.

Variants and properties: The kohdemedian is nonparametric and robust to outliers within the non-targeted portion of the data, since those observations do not contribute to S. It reduces to the ordinary median when T covers all observations. A weighted version can be defined by assigning weights w_i to observations, yielding a weighted kohdemedian that emphasizes targeted observations more strongly.

Applications: It is used in segment-focused analysis, performance reporting, and decision support where a summary statistic should reflect a specific subset of data. For example, analysts might compute the kohdemedian of sales x_i for stores within a target region T, ignoring other stores to obtain a regional central tendency.

See also: median, weighted median, robust statistics, targeted analysis.