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Using Norms to Understand Linear Regression

Introduction In my last post, I described how we can derive modes, medians and means as three natural solutions to the problem of summarizing a list of numbers, \((x_1, x_2, \ldots, x_n)\), using a single number, \(s\). In particular, we measured the quality of different potential summaries in three different ways, which led us to […]

Modes, Medians and Means: A Unifying Perspective

Modes, Medians and Means: A Unifying Perspective

Introduction / Warning Any traditional introductory statistics course will teach students the definitions of modes, medians and means. But, because introductory courses can’t assume that students have much mathematical maturity, the close relationship between these three summary statistics can’t be made clear. This post tries to remedy that situation by making it clear that all […]