Math - 2 months ago 15

R Question

I have

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

With

`boxplot`

`quantile(X,0.25)`

`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)

Do you know why?

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")
```