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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
Pattern of latter two bullet points: If there are no data points at the true quartiles, use data points slightly "inland" (closer to the median) from the actual quartiles. This means the 1.5*IQR whiskers can be uneven in lengths. The median, minimum, maximum, and the first and third quartile constitute the Five-number summary. [9]
Splitting the observations either side of the median gives two groups of four observations. The median of the first group is the lower or first quartile, and is equal to (0 + 1)/2 = 0.5. The median of the second group is the upper or third quartile, and is equal to (27 + 61)/2 = 44. The smallest and largest observations are 0 and 63.
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 ...
The bold numbers (36, 39) are used to calculate the median as their average. As there are an even number of data points, the first three methods all give the same results. (The Method 3 is executed such that the median is not chosen as a new data point and the Method 1 started.)
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.
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Firstly, computing median of an odd list is faster and simpler; while one could use an even list, this requires taking the average of the two middle elements, which is slower than simply selecting the single exact middle element. Secondly, five is the smallest odd number such that median of medians works.
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