Sample Median Function

A Sample Median Function is a Median Function that is a Sample Statistic Function (based on a Random Sample).

• • …
• Counter-Example(s):
  • Arithmetic Median Function.
  • Sample Mean.
  • Sample Mode.
  • Sample Geometric Mean.
• See: Sample Variance.

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References

2013

• http://en.wikipedia.org/wiki/Median#Medians_for_samples
  • Even though sorting n items requires O(n log n) operations, selection algorithms can compute the k^th-smallest of n items (e.g., the median) with only O(n) operations.
  • In individual series (if number of observation is very low) first one must arrange all the observations in ascending order. Then count(n) total number of observation in given data.

    If n is odd then Median (M) = value of ((n + 1)/2)th item term.

    If n is even then Median (M) = value of [((n)/2)th item term + ((n)/2 + 1)th item term ]/2

    For an odd number of values

    As an example, we will calculate the sample median for the following set of observations: 1, 5, 2, 8, 7. Start by sorting the values: 1, 2, 5, 7, 8. In this case, the median is 5 since it is the middle observation in the ordered list.

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Median
  • In probability theory and statistics, a median is described as the number separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, the median is not unique, so one often takes the mean of the two middle values. At most half the population have values less than the median and at most half have values greater than the median. If both groups contain less than half the population, then some of the population is exactly equal to the median. For example, if a < b < c, then the median of the list {a, b, c} is b, and if a < b < c < d, then the median of the list {a, b, c, d} is the mean of b and c, i.e. it is (b + c)/2.
  • The median can be used when a distribution is skewed, when end values are not known, or when outliers likely represent measurement errors. A disadvantage is the difficulty of handling it theoretically
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Centerpoint_(geometry)
  • In statistics and computational geometry, the centerpoint is a generalization of the median to data in two or more dimensions. Given a set of points, any hyperplane that goes through a centerpoint divides the points in two roughly equal parts: the smaller part should have at least a 1/(d + 1) fraction of the points. Like the median, a centerpoint need not be one of the data points. Any set of points (with no duplicates) has at least one centerpoint. Closely related concepts are the Tukey depth of a point (the minimum number of sample points on one side of a hyperplane through the point) and the Tukey median of a point set (the point maximizing the Tukey depth). A centerpoint is a point of depth at least n/(d + 1), and a Tukey median must be a centerpoint, but not every centerpoint is a Tukey median.
  • In computational geometry, the centerpoint helps to produce divide and conquer algorithms.

1978

• J. S. Maritza & R. G. Jarretta. (1978). “A Note on Estimating the Variance of the Sample Median.” In: Journal of the American Statistical Association, 73(361). doi:10.1080/01621459.1978.10480027

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