For a finite first absolute moment, the minimizers of expected absolute loss are the medians. With a density, differentiating the loss gives , so every point where the cumulative distribution function equals one half minimizes it. A density gap may give a whole minimizing interval. In contrast, finite squared loss is uniquely minimized by the expectation.
The sample median is the middle order statistic for an odd sample size and any conventional midpoint of the two central order statistics for an even sample size.
The coordinatewise median of vectors applies the univariate sample median separately to each coordinate. It is easy to compute but depends on the chosen coordinate axes.
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The median is a measure of central tendency that represents the middle value of a dataset when the values are arranged in ascending or descending order. To find the median: 1. **Organize the Data**: Arrange the numbers in the dataset from smallest to largest (or largest to smallest). 2. **Count the Observations**: - If there is an **odd number** of observations, the median is the middle number.