Sample median | Wikipedia audio article

This is an audio version of the Wikipedia Article:
en.wikipedia.org/wiki/Median


00:01:17 1 Finite set of numbers
00:03:53 2 Probability distributions
00:05:50 2.1 Medians of particular distributions
00:07:08 3 Populations
00:08:26 3.1 Optimality property
00:09:05 3.2 Unimodal distributions
00:10:23 3.3 Inequality relating means and medians
00:12:20 4 Jensen's inequality for medians
00:15:34 5 Medians for samples
00:16:52 5.1 The sample median
00:17:31 5.1.1 Efficient computation of the sample median
00:18:10 5.1.2 Easy explanation of the sample median
00:19:28 5.1.3 Sampling distribution
00:20:46 5.2 Other estimators
00:22:04 5.3 Coefficient of dispersion
00:23:22 6 Multivariate median
00:31:09 6.1 Marginal median
00:32:27 6.2 Centerpoint
00:33:45 7 Other median-related concepts
00:37:00 7.1 Interpolated median
00:38:18 7.2 Pseudo-median
00:39:36 7.3 Variants of regression
00:40:53 7.4 Median filter
00:41:32 7.5 Cluster analysis
00:43:29 7.6 Median–median line
00:44:47 8 Median-unbiased estimators
00:46:05 9 History
00:47:23 10 See also
00:48:41 11 References
00:49:59 12 External links
00:51:17 History
00:52:35 See also



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SUMMARY
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The median is the value separating the higher half from the lower half of a data sample (a population or a probability distribution). For a data set, it may be thought of as the "middle" value. For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6, the fourth largest, and also the fourth smallest, number in the sample. For a continuous probability distribution, the median is the value such that a number is equally likely to fall above or below it.
The median is a commonly used measure of the properties of a data set in statistics and probability theory. The basic advantage of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed so much by a small proportion of extremely large or small values, and so it may give a better idea of a "typical" value. For example, in understanding statistics like household income or assets, which vary greatly, the mean may be skewed by a small number of extremely high or low values. Median income, for example, may be a better way to suggest what a "typical" income is.
Because of this, the median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median will not give an arbitrarily large or small result.