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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
These are the number of moons of each planet in the Solar System. It helps to put the observations in ascending order: 0, 0, 1, 2, 13, 27, 61, 63. There are eight observations, so the median is the mean of the two middle numbers, (2 + 13)/2 = 7.5. Splitting the observations either side of the median gives two groups of four observations.
The median of medians method partitions the input into sets of five elements, and uses some other non-recursive method to find the median of each of these sets in constant time per set. It then recursively calls itself to find the median of these n / 5 {\displaystyle n/5} medians.
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.
It has a median value of 2. The absolute deviations about 2 are (1, 1, 0, 0, 2, 4, 7) which in turn have a median value of 1 (because the sorted absolute deviations are (0, 0, 1, 1, 2, 4, 7)). So the median absolute deviation for this data is 1.
The weighted median can be computed by sorting the set of numbers and finding the smallest set of numbers which sum to half the weight of the total weight. This algorithm takes () time. There is a better approach to find the weighted median using a modified selection algorithm. [1]
Median cut is an algorithm to sort data of an arbitrary number of dimensions into series of sets by recursively cutting each set of data at the median point along the longest dimension. Median cut is typically used for color quantization. For example, to reduce a 64k-colour image to 256 colours, median cut is used to find 256 colours that match ...
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.