(Weighted) Median Value

Compute the sample median. The function basically wraps the function quantileX(), which offers the option to define weights.
For grouped data the median can be estimated by linear interpolation within the class containing the median, which is implemented in the interface for Freq-objects.

Usage

medianX(x, ...)

# Default S3 method
medianX(x, weights = NULL, na.rm = FALSE, ...)

# S3 method for class 'factor'
medianX(x, weights = NULL, na.rm = FALSE, ...)

# S3 method for class 'Freq'
medianX(x, breaks, ...)

Arguments

x: an object for which a method has been defined, or a numeric vector containing the values whose median is to be computed
...: further arguments passed to stats::median() in the unweighted default method, otherwise unused
weights: a numerical vector of weights the same length as x giving the weights to use for elements of x. Only the ratios of the weights matter (see Details); frequency weights reproduce the median of the replicated sample. Supported for numeric x only.
na.rm: a logical value indicating whether NA values should be stripped before the computation proceeds
breaks: breaks for calculating the median for classified data as composed by freq(); strictly increasing, one more than there are classes. If the median falls into an open-ended class (-Inf or Inf as a bound), NA is returned with a warning.

Value

the unweighted default method returns a length-one object of the same type as x, except when x is integer of even length, when the result will be double. With weights the result is double.

If there are no values or if na.rm = FALSE and there are NA values the result is NA of the same type as x (or more generally the result of x[FALSE][NA]). For ordered factors, missing results retain the ordered-factor class and the original levels.

Details

This is a generic function for which methods can be written. However, the default method makes use of is.na, sort and mean from package base all of which are generic, and so the default method will work for most classes (e.g., "[Date]") for which a median is a reasonable concept.

For ordered factors, the result is the upper sample median: the category at position floor(n / 2) + 1 in the sorted non-missing observations. If the two middle observations of an even-sized sample differ, a warning is issued. Their integer level codes are not averaged, because distances between ordinal categories are not defined. Unused levels are preserved and cannot become the median merely by lying between observed categories. Unordered factors are rejected.

Note

There are alternative approaches for calculating weighted median (e.g. matrixstats::weightedMedian).

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Examples


medianX(1:4)                # = 2.5 [even number]
#> [1] 2.5
medianX(c(1:3, 100, 1000))  # = 3 [odd, robust]
#> [1] 3

# Approximation for classified data
breaks <- seq(10,70, 10)
medianX(
  freq(cut(Pizza$temperature, breaks=breaks)),
  breaks=breaks)
#> [1] 49.91404

# compared to
medianX(Pizza$temperature)
#> [1] NA

# starting from a classified table
# from     to  income
#    0   4000      20
# 4000   6000      42
# 6000   8000      31
# 8000  10000      12

# freq(as.table(c(20,42,31,12)))
#    level  freq   perc  cumfreq  cumperc
# 1      A    20  19.0%       20    19.0%
# 2      B    42  40.0%       62    59.0%
# 3      C    31  29.5%       93    88.6%
# 4      D    12  11.4%      105   100.0%

medianX(freq(as.table(c(20,42,31,12))), breaks=c(0,4000,6000,8000,10000))
#> [1] 5547.619

# use weights
x <- sample(20, 30, replace = TRUE)
z <- as.numeric(names(w <- table(x)))

(m1 <- medianX(z, weights=w))
#> [1] 8.5
(m2 <- medianX(x))
#> [1] 8.5
stopifnot(identical(m1, m2))