Understanding the pitfalls of preferring the median over the mean

A common task in mathematical statistics is to aggregate a set of numbers \(\mathbf{x} = \{ x_1, x_2, \ldots, x_n \}\) to a single “average” value. Such a value is usually called central tendency. There are multiple measures of central tendency. The most popular one is the arithmetic average or the mean: \[\overline{\mathbf{x}} = \left( x_1 + x_2 + \ldots + x_n \right) / n. \] The mean is so popular not only thanks to its simplicity but also because it provides the best way to estimate the cente...

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