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Median. Finding the median in sets of data with an odd and even number of values. The median of a set of numbers 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.
Median of medians. In computer science, the median of medians is an approximate median selection algorithm, frequently used to supply a good pivot for an exact selection algorithm, most commonly quickselect, that selects the k th smallest element of an initially unsorted array. Median of medians finds an approximate median in linear time.
The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic, being more resilient to outliers in a data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it.
If there are an odd number of data points in the original ordered data set, include the median (the central value in the ordered list) in both halves. If there are an even number of data points in the original ordered data set, split this data set exactly in half. The lower quartile value is the median of the lower half of the data. The upper ...
Selection algorithm. In computer science, a selection algorithm is an algorithm for finding the th smallest value in a collection of ordered values, such as numbers. The value that it finds is called the th order statistic. Selection includes as special cases the problems of finding the minimum, median, and maximum element in the collection.
The median is the most trimmed statistic (nominally 50%), as it discards all but the most central data, and equals the fully trimmed mean – or indeed fully trimmed mid-range, or (for odd-size data sets) the fully trimmed maximum or minimum. Likewise, no degree of trimming has any effect on the median – a trimmed median is the median ...
The sample median may or may not be an order statistic, since there is a single middle value only when the number n of observations is odd. More precisely, if n = 2 m +1 for some integer m , then the sample median is X ( m + 1 ) {\displaystyle X_{(m+1)}} and so is an order statistic.
Deviation (statistics) Plot of standard deviation of a random distribution. In mathematics and statistics, deviation serves as a measure to quantify the disparity between an observed value of a variable and another designated value, frequently the mean of that variable. Deviations with respect to the sample mean and the population mean (or ...