(Weighted) Median Value

Compute the sample median. The function basically wraps the function Quantile(), 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.

Median(x, ...)

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

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

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

Arguments

x

an object for which a method has been defined, or a numeric vector containing the values whose median is to be computed.

weights

a numerical vector of weights the same length as x giving the weights to use for elements of x.

breaks

breaks for calculating the mean for classified data as composed by Freq.

na.rm

a logical value indicating whether NA values should be stripped before the computation proceeds.

...

further arguments passed to or from other methods.

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

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]).

References

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

See also

quantile for general quantiles. https://stat.ethz.ch/pipermail/r-help/2003-November/042684.html

https://stackoverflow.com/questions/7925102/idiomatic-method-of-finding-the-median-of-an-ordinal

Examples

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

# Approximation for classified data
breaks <- seq(10,70, 10)
Median(
  Freq(cut(d.pizza$temperature, breaks=breaks)),
  breaks=breaks)
#> [1] 49.91404

# compared to
Median(d.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%

Median(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 <- Median(z, weights=w))
#> [1] 9
(m2 <- Median(x))
#> [1] 9
stopifnot(identical(m1, m2))