compute the median
Data Set Options
Random Variable Options
data set or Matrix data set
algebraic; random variable or distribution
(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the median of a data set
(optional) equation of the form numeric=value; specifies options for computing the median of a random variable
The Median function computes the median of the specified random variable or data set.
The first parameter can be a data set (e.g., a Vector), a Matrix data set, a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
In the first calling sequence, if A has an even number of data points, then the median is the mean of the two middle data points.
In the second calling sequence, if X is a discrete random variable, then the median is defined as the first point t such that the CDF at t is greater than or equal to 12.
By default, all computations involving random variables are performed symbolically (see option numeric below).
All computations involving data are performed in floating-point; therefore, all data provided must have type/realcons and all returned solutions are floating-point, even if the problem is specified with exact values.
For more information about computation in the Statistics package, see the Statistics[Computation] help page.
The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.
ignore=truefalse -- This option controls how missing data is handled by the Median command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Median command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.
weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight 1.
The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.
numeric=truefalse -- By default, the median is computed using exact arithmetic. To compute the median numerically, specify the numeric or numeric = true option.
Compute the median of the Weibull distribution with parameters p and q.
Use numeric parameters.
Generate a random sample of size 100000 drawn from the above distribution and compute the sample median.
A ≔ Sample⁡Weibull⁡3,5,105:
Compute the standard error of the sample median for the normal distribution with parameters 5 and 2.
X ≔ Normal⁡5,2
B ≔ Sample⁡X,106:
Compute the median of a sum of two random variables.
X ≔ RandomVariable⁡Normal⁡5,2:
Y ≔ RandomVariable⁡Normal⁡10,1:
Verify this using simulation.
C ≔ Sample⁡X+Y,105:
Compute the median of a weighted data set.
V ≔ seq⁡i,i=57..77,undefined:
W ≔ 2,4,14,41,83,169,394,669,990,1223,1329,1230,1063,646,392,202,79,32,16,5,2,5:
Consider the following Matrix data set.
M ≔ Matrix⁡3,1130,114694,4,1527,127368,3,907,88464,2,878,96484,4,995,128007
We compute the median of each of the columns.
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
The A parameter was updated in Maple 16.
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