(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, 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 or from other methods
weights: a numerical vector of weights the same length as x giving the weights to use for elements of x
na.rm: a logical value indicating whether NA values should be stripped before the computation proceeds
breaks: breaks for calculating the mean for classified data as composed by freq()

Value

the 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.

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]).

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.

Calculating the median for ordered factors is not implemented in standard R, as it's not well defined (it is not clear what to do if the median sits between two levels in factors of even length). This function returns the high median and prints a warning if the low median would be different (which is supposed to be a rare event). There's a vivid discussion between experts going on whether this should be defined or not. We'll wait for definitive results and enjoy the function's comfort so far...

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))