(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, ...)
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 |
breaks |
breaks for calculating the mean for classified data as composed by |
na.rm |
a logical value indicating whether |
... |
further arguments passed to or from other methods. |
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).
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]).
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
quantile for general quantiles.
https://stat.ethz.ch/pipermail/r-help/2003-November/042684.html
Median(1:4) # = 2.5 [even number] Median(c(1:3, 100, 1000)) # = 3 [odd, robust] # Approximation for classified data breaks <- seq(10,70, 10) Median( Freq(cut(d.pizza$temperature, breaks=breaks)), breaks=breaks) # compared to Median(d.pizza$temperature) # 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)) # use weights x <- sample(20, 30, replace = TRUE) z <- as.numeric(names(w <- table(x))) (m1 <- Median(z, weights=w)) (m2 <- Median(x)) stopifnot(identical(m1, m2))
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