Physics – Data Analysis – Statistics and Probability
Scientific paper
2008-04-03
Physics
Data Analysis, Statistics and Probability
22 pages, no figure
Scientific paper
The sample median is often used in statistical analyses of physical or astronomical data wherein a central value must be found from samples polluted by elements which do not belong to the population of interest or when the underlying probability law is such that the sample mean is useless for the stated purpose. Although it does not generally possesses the nice linearity properties of the mean, the median has advantages of its own, some of which are explored in this paper which elucidates analogies and differences between these two central value descriptors. Some elementary results are shown, most of which are certainly not new but not widely known either. It is observed that the moment and the quantile approaches to the description of a probability distribution are difficult to relate, but that when the quantile description is used, the sample median can be characterized very much in the same way as the sample mean; this opens the possibility of using it for estimation purposes beyond what is usually done. In order to relate the two approaches, a derivation is given of the asymptotic joint distribution of the mean and the median for a general continuous probability law.
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