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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 (after arranging in ascending order). For example, the following list of seven numbers, 1, 3, 3, 6, 7, 8, 9
The five-number summary gives information about the location (from the median), spread (from the quartiles) and range (from the sample minimum and maximum) of the observations. Since it reports order statistics (rather than, say, the mean) the five-number summary is appropriate for ordinal measurements , as well as interval and ratio measurements.
Use the median to divide the ordered data set into two halves. The median becomes the second quartile. If there are an odd number of data points in the original ordered data set, do not include the median (the central value in the ordered list) in either half.
The median is the middle number of the group when they are ranked in order. (If there are an even number of numbers, the mean of the middle two is taken.) Thus to find the median, order the list according to its elements' magnitude and then repeatedly remove the pair consisting of the highest and lowest values until either one or two values are ...
With an odd number of observations, the median is the middle observation, and the quartiles are the medians of the lower resp. upper half of the observations, omitting the middle one. With an even number of observations, the median is the mean of the two middle observations, and the quartiles are the medians of the lower resp. upper half of the ...
Annual median equivalised disposable income per person, by OECD country. [2]The median equivalised disposable income is the median of the disposable income which is equivalised by dividing income by the square root of household size; the square root is used to acknowledge that people sharing accommodation benefit from pooling at least some of their living costs.
The median is also very robust in the presence of outliers, while the mean is rather sensitive. In continuous unimodal distributions the median often lies between the mean and the mode, about one third of the way going from mean to mode. In a formula, median ≈ (2 × mean + mode)/3.
Median the middle value that separates the higher half from the lower half of the data set. The median and the mode are the only measures of central tendency that can be used for ordinal data, in which values are ranked relative to each other but are not measured absolutely. Mode the most frequent value in the data set.