2024 , Volume 29, № 4, p.55-70

Purpose. Define the median of the interval sample as a statistical characteristic of the sample elements, generalizing the definition of the median for point data.

Methodology. To determine the median of an interval sample, it is necessary to set a linear order relation for interval data and determine the frequency of occurrence in the sample for them. We solve this problem by switching from the initial sampling intervals to a minimal set of their subintervals (elementary subintervals), sampling intervals can be obtained by combining these subintervals. A generalized definition of the median for point data is carried out by us in compliance with the correspondence principle: when the interval widths tend to zero, the median value calculated for the intervals will tend to the median value of the sample of point values to which the narrowed intervals tend.

Findings. The median of the sample with interval elements is determined. This definition is a natural generalization of both the usual definition of the sample median as the middle value in a variation series composed of sample elements and the definition of the median of grouped data.

Originality/value. The interval median defined in the paper can be used to estimate the distribution of interval empirical data through their median value and for centering and normalization of interval data. If the value specified with interval uncertainty is guaranteed to take on all possible values from given sampling intervals and does not have only one true value for each sampling interval, the interval median determined in the paper turns out to be more adequate for estimating the middle value than the median determined by the ends of the sampling intervals.