The Median The Median In statistics and probability theory, median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values.

A median is only defined on one-dimensional data, and is independent of any distance metric. A geometric median, on the other hand, is defined in any number of dimensions. In a sample of data, or a finite population, there may be no member of the sample whose value is identical to the median (in the case of an even sample size), and, if there is such a member, there may be more than one so that the median may not uniquely identify a sample member. Know More About Frequency Distributions Math.Tutorvista.com

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Nonetheless, the value of the median is uniquely determined with the usual definition. A related concept, in which the outcome is forced to correspond to a member of the sample, is the medoid. At most, half the population have values strictly less than the median, and, at most, half have values strictly greater than the median. If each group contains less than half the population, then some of the population is exactly equal to the median. For example, if a < b < c, then the median of the list {a, b, c} is b. If a <> b <> c as well, then only a is strictly less than the median, and only c is strictly greater than the median. Since each group is less than half (one-third, in fact), the leftover b is strictly equal to the median (a truism). Likewise, if a < b < c < d, then the median of the list {a, b, c, d} is the mean of b and c; i.e., it is (b + c)/2. The median can be used as a measure of location when a distribution is skewed, when end-values are not known, or when one requires reduced importance to be attached to outliers, e.g., because they may be measurement errors. In terms of notation, some authors represent the median of a variable x either as or as There is no simple, widely accepted standard notation for the median. so the use of these or other symbols for the median needs to be explicitly defined when they are introduced. Learn More Data Graphs Math.Tutorvista.com

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The sample median Even though sorting n items requires O(n log n) operations, selection algorithms can compute the kth-smallest of n items (e.g., the median) with only O(n) operations.[8] In individual series (if number of observation is very low) first one must arrange all the observations in ascending order. Then count(n) total number of observation in given data. If n is odd then Median (M) = value of ((n + 1)/2)th item term. If n is even then Median (M) = value of [((n)/2)th item term + ((n)/2 + 1)th item term ]/2

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The Median

Published on May 28, 2012

In a sample of data, or a finite population, there may be no member of the sample whose value is identical to the median (in the case of an...

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