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The median of a finite list of numbers is the "middle" number, when those numbers are listed in order from smallest to greatest. If the data set has an odd number of observations, the middle one is selected. For example, the following list of seven numbers, has the median of 6, which is the fourth value.
the arithmetic mean of the maximum and minimum values of a data set. Midhinge the arithmetic mean of the first and third quartiles. Quasi-arithmetic mean A generalization of the generalized mean, specified by a continuous injective function. Trimean the weighted arithmetic mean of the median and two quartiles. Winsorized mean
The mean of a set of observations is the arithmetic average of the values; however, for skewed distributions, the mean is not necessarily the same as the middle value (median), or the most likely value (mode). For example, mean income is typically skewed upwards by a small number of people with very large incomes, so that the majority have an ...
Mid-range. In statistics, the mid-range or mid-extreme is a measure of central tendency of a sample defined as the arithmetic mean of the maximum and minimum values of the data set: [ 1] The mid-range is closely related to the range, a measure of statistical dispersion defined as the difference between maximum and minimum values.
For the music theory concept of "modes", see Mode (music). In statistics, the mode is the value that appears most often in a set of data values. [ 1 ] If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e., x=argmaxxi P (X = xi) ). In other words, it is the value that is ...
m(X) is the chosen measure of central tendency of the data set—sometimes the mean (¯), but most often the median. The average absolute deviation (AAD) in statistics is a measure of the dispersion or spread of a set of data points around a central value, usually the mean or median.
Definition. The arithmetic mean of a set of observed data is equal to the sum of the numerical values of each observation, divided by the total number of observations. Symbolically, for a data set consisting of the values , the arithmetic mean is defined by the formula: [ 2] (For an explanation of the summation operator, see summation .)
Average absolute deviation. The average absolute deviation ( AAD) of a data set is the average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be a mean, median, mode, or the result of any other measure of central tendency or any ...