Math Math - 17 days ago 6
R Question

lower and upper quartiles in boxplot in R

I have

X=c(20 ,18, 34, 45, 30, 51, 63, 52, 29, 36, 27, 24)


With
boxplot
, i'm trying to plot the
quantile(X,0.25)
and
quantile(X,0.75)

but this is not realy the same lower and upper quartiles in boxplot in R

boxplot(X)
abline(h=quantile(X,0.25),col="red",lty=2)
abline(h=quantile(X,0.75),col="red",lty=2)


enter image description here
Do you know why?

lmo lmo
Answer

The values of the box are called hinges and may coincide with the quartiles (as calculated by quantile(x, c(0.25, .075))), but are calculated differently.

From ?boxplot.stats:

The two ‘hinges’ are versions of the first and third quartile, i.e., close to quantile(x, c(1,3)/4). The hinges equal the quartiles for odd n (where n <- length(x)) and differ for even n. Whereas the quartiles only equal observations for n %% 4 == 1 (n = 1 mod 4), the hinges do so additionally for n %% 4 == 2 (n = 2 mod 4), and are in the middle of two observations otherwise.

To see that the values coincide with an odd number of observations, try the following code:

set.seed(1234)
x <- rnorm(9)

boxplot(x)
abline(h=quantile(x, c(0.25, 0.75)), col="red")

enter image description here

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