Solved – Missing quartile in boxplot

boxplotdescriptive statistics

Currently I am creating a box plot. I am new on the field of statistics and especially box plots. Find the picture following:

On the y-axis find the number of messages. I have problems understanding what I see there. The plot is created by Matlab automatically. As I know there should be four quartile in a box plot. I see there only three. Probably this happened because of the value of the median (it is the green line). But I do not know what this means if a quartile is missing. Is somebody around here who can may be explain this and tell me some details, what you can read out of the plot?

Best Answer

The median is probably identical to the first quartile, which is why they overlap. This tends to happen when you have a large proportion of identical, low values in the dataset. Here's an example that reproduces this pattern:

dat <- c(1,2,2,2,3,5,6)

median(dat)
## 2
quantile(dat, 0.25)
## 25% 
##  2 

boxplot(dat)

You can read a basic introduction about how to interpret boxplots here. Though as Nick Cox points out below, its discussion of what are called 'outliers' is flawed and should be ignored. Outliers should not be deleted unless there is very strong reason to, such as a clear data recording error.

Note also that a boxplot is not a great way to display many datasets. I agree with Stephan Kolassa's recommendation of a beeswarm plot for small datasets and a violin plot/kernel density plot for larger ones.

Related Solutions

Solved – Boxplot for data with a large number of zero values

You can use violin plots and logarithmic transformation (of course you should add some constant to avoid $log(0)$) to compare the distributions and their quantiles at different levels of some factor.

For the sake of illustration please see below zero-inflated data of the number of the cod parasite (A Beginner’s Guide to R, A.F. Zuur et al., 2009) in dependence of its sex:

df <- structure(list(Sex = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 1L, 1L, 1L, 2L, 1L, 
2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 
2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 
2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 
1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 
2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 
1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 
2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 
1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 
2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 
2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 
1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 
1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 
1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 
2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 
1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 
2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 0L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 
1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 
2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 
1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 
1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 
1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 
2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 
1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 
1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 
1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 
1L, 2L, 2L, 1L, 0L, 0L, 0L, 0L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 
1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 0L, 0L, 1L, 2L, 1L, 2L, 
2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 
2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 0L, 0L, 1L, 1L, 2L, 
2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 
0L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 
2L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 0L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 0L, 1L, 1L, 2L, 1L, 
2L, 2L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 
1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 
2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 0L, 0L, 
2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 0L, 2L, 1L, 0L, 0L, 1L, 1L, 0L, 
2L, 0L, 2L, 0L, 1L, 0L, 0L, 2L, 2L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 
2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 
1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 
2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 
1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 
1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 
2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 
1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 
2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 
2L, 2L, 2L), Intensity = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 
10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 12L, 12L, 12L, 12L, 
12L, 12L, 12L, 13L, 13L, 13L, 14L, 14L, 14L, 14L, 15L, 15L, 15L, 
16L, 16L, 16L, 16L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 19L, 19L, 
20L, 20L, 21L, 21L, 21L, 22L, 22L, 23L, 23L, 24L, 25L, 25L, 26L, 
27L, 28L, 28L, 28L, 32L, 33L, 35L, 35L, 36L, 38L, 39L, 41L, 41L, 
45L, 50L, 51L, 52L, 56L, 65L, 68L, 73L, 84L, 86L, 126L, 160L, 
183L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 6L, 6L, 6L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
9L, 9L, 9L, 10L, 10L, 11L, 11L, 12L, 12L, 12L, 12L, 13L, 14L, 
14L, 14L, 15L, 17L, 19L, 20L, 20L, 22L, 26L, 26L, 27L, 28L, 30L, 
30L, 30L, 31L, 31L, 35L, 39L, 40L, 43L, 43L, 44L, 45L, 45L, 49L, 
52L, 56L, 56L, 58L, 67L, 67L, 71L, 81L, 186L, 210L, 223L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 10L, 
10L, 10L, 10L, 10L, 11L, 13L, 13L, 13L, 14L, 14L, 14L, 16L, 17L, 
17L, 18L, 18L, 18L, 19L, 20L, 20L, 30L, 34L, 36L, 40L, 42L, 45L, 
46L, 46L, 49L, 50L, 55L, 75L, 84L, 89L, 90L, 104L, 125L, 128L, 
257L)), class = "data.frame", row.names = c(1L, 2L, 3L, 4L, 5L, 
6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 
19L, 20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 
32L, 33L, 34L, 35L, 36L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L, 
45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 
58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 68L, 69L, 70L, 
71L, 72L, 73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 81L, 82L, 83L, 
84L, 85L, 86L, 87L, 88L, 89L, 90L, 91L, 92L, 93L, 94L, 95L, 96L, 
97L, 98L, 99L, 100L, 101L, 102L, 103L, 104L, 105L, 106L, 107L, 
108L, 109L, 110L, 111L, 112L, 113L, 114L, 115L, 116L, 117L, 118L, 
119L, 120L, 121L, 122L, 123L, 124L, 125L, 126L, 127L, 128L, 129L, 
130L, 131L, 132L, 133L, 134L, 135L, 136L, 137L, 138L, 139L, 140L, 
141L, 142L, 143L, 144L, 145L, 146L, 147L, 148L, 149L, 150L, 151L, 
152L, 153L, 154L, 155L, 156L, 157L, 158L, 159L, 160L, 161L, 162L, 
163L, 164L, 165L, 166L, 167L, 168L, 169L, 170L, 171L, 172L, 173L, 
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185L, 186L, 187L, 188L, 189L, 190L, 191L, 192L, 193L, 194L, 195L, 
196L, 197L, 198L, 199L, 200L, 201L, 202L, 203L, 204L, 205L, 206L, 
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240L, 241L, 242L, 243L, 244L, 245L, 246L, 247L, 248L, 249L, 250L, 
251L, 252L, 253L, 254L, 255L, 256L, 257L, 258L, 259L, 260L, 261L, 
262L, 263L, 264L, 265L, 266L, 267L, 268L, 269L, 270L, 271L, 272L, 
273L, 274L, 275L, 276L, 277L, 278L, 279L, 280L, 281L, 282L, 283L, 
284L, 285L, 286L, 287L, 288L, 289L, 290L, 291L, 292L, 293L, 294L, 
295L, 296L, 297L, 298L, 299L, 300L, 301L, 302L, 303L, 304L, 305L, 
306L, 307L, 308L, 309L, 310L, 311L, 312L, 313L, 314L, 315L, 316L, 
317L, 318L, 319L, 320L, 321L, 322L, 323L, 324L, 325L, 326L, 327L, 
328L, 329L, 330L, 331L, 332L, 333L, 334L, 335L, 336L, 337L, 338L, 
339L, 340L, 341L, 342L, 343L, 344L, 345L, 346L, 347L, 348L, 349L, 
350L, 351L, 352L, 353L, 354L, 355L, 356L, 357L, 358L, 359L, 360L, 
361L, 362L, 363L, 364L, 365L, 366L, 367L, 368L, 369L, 370L, 371L, 
372L, 373L, 374L, 375L, 376L, 377L, 378L, 379L, 380L, 381L, 382L, 
383L, 384L, 385L, 386L, 387L, 388L, 389L, 390L, 391L, 392L, 393L, 
394L, 395L, 396L, 397L, 398L, 399L, 400L, 401L, 402L, 403L, 404L, 
405L, 406L, 407L, 408L, 409L, 410L, 411L, 412L, 413L, 414L, 415L, 
416L, 417L, 418L, 419L, 420L, 421L, 422L, 423L, 424L, 425L, 426L, 
427L, 428L, 429L, 430L, 431L, 432L, 433L, 434L, 435L, 436L, 437L, 
438L, 439L, 440L, 441L, 442L, 443L, 444L, 445L, 446L, 447L, 448L, 
449L, 450L, 451L, 452L, 453L, 454L, 455L, 456L, 457L, 458L, 459L, 
460L, 461L, 462L, 463L, 464L, 465L, 466L, 467L, 468L, 469L, 470L, 
471L, 472L, 473L, 474L, 475L, 476L, 477L, 478L, 479L, 480L, 481L, 
482L, 483L, 484L, 485L, 486L, 487L, 488L, 489L, 490L, 491L, 492L, 
493L, 494L, 495L, 496L, 497L, 498L, 499L, 500L, 501L, 502L, 503L, 
504L, 505L, 506L, 507L, 508L, 509L, 510L, 511L, 512L, 513L, 514L, 
515L, 516L, 517L, 518L, 519L, 520L, 521L, 522L, 523L, 524L, 525L, 
526L, 527L, 528L, 529L, 530L, 531L, 532L, 533L, 534L, 535L, 536L, 
537L, 538L, 539L, 540L, 541L, 542L, 543L, 544L, 545L, 546L, 547L, 
548L, 549L, 550L, 551L, 552L, 553L, 554L, 555L, 556L, 557L, 558L, 
559L, 560L, 561L, 562L, 563L, 564L, 565L, 566L, 567L, 568L, 569L, 
570L, 571L, 572L, 573L, 574L, 575L, 576L, 577L, 578L, 579L, 580L, 
581L, 582L, 583L, 584L, 585L, 586L, 587L, 588L, 589L, 590L, 591L, 
592L, 593L, 594L, 595L, 596L, 597L, 598L, 599L, 600L, 601L, 602L, 
603L, 604L, 605L, 606L, 607L, 608L, 609L, 610L, 611L, 612L, 613L, 
614L, 615L, 616L, 617L, 618L, 619L, 620L, 621L, 622L, 623L, 624L, 
625L, 626L, 627L, 628L, 629L, 630L, 631L, 632L, 633L, 634L, 635L, 
636L, 637L, 638L, 639L, 640L, 641L, 642L, 643L, 644L, 645L, 646L, 
647L, 648L, 649L, 650L, 651L, 652L, 653L, 654L, 655L, 656L, 657L, 
658L, 659L, 660L, 661L, 662L, 663L, 664L, 665L, 666L, 667L, 668L, 
669L, 670L, 671L, 672L, 673L, 674L, 675L, 676L, 677L, 678L, 679L, 
680L, 681L, 682L, 683L, 684L, 685L, 686L, 687L, 688L, 689L, 690L, 
691L, 692L, 693L, 694L, 695L, 696L, 697L, 698L, 699L, 700L, 701L, 
702L, 703L, 704L, 705L, 706L, 707L, 708L, 709L, 710L, 711L, 712L, 
713L, 714L, 715L, 716L, 717L, 718L, 719L, 720L, 721L, 722L, 723L, 
724L, 725L, 726L, 727L, 728L, 729L, 730L, 731L, 732L, 733L, 734L, 
735L, 736L, 737L, 738L, 739L, 740L, 741L, 742L, 743L, 744L, 745L, 
746L, 747L, 748L, 749L, 750L, 751L, 752L, 753L, 754L, 755L, 756L, 
757L, 758L, 759L, 760L, 761L, 762L, 763L, 764L, 765L, 766L, 767L, 
768L, 769L, 770L, 771L, 772L, 773L, 774L, 775L, 776L, 777L, 778L, 
779L, 780L, 781L, 782L, 783L, 784L, 785L, 786L, 787L, 788L, 789L, 
790L, 791L, 792L, 793L, 794L, 795L, 796L, 797L, 798L, 799L, 800L, 
801L, 802L, 803L, 804L, 805L, 806L, 807L, 808L, 809L, 810L, 811L, 
812L, 813L, 814L, 815L, 816L, 817L, 818L, 819L, 820L, 821L, 822L, 
823L, 824L, 825L, 826L, 827L, 828L, 829L, 830L, 831L, 832L, 833L, 
834L, 835L, 836L, 837L, 838L, 839L, 840L, 841L, 842L, 843L, 844L, 
845L, 846L, 847L, 848L, 849L, 850L, 851L, 852L, 853L, 854L, 855L, 
856L, 857L, 858L, 859L, 860L, 861L, 862L, 863L, 864L, 865L, 866L, 
867L, 868L, 869L, 870L, 871L, 872L, 873L, 874L, 875L, 876L, 877L, 
878L, 879L, 880L, 881L, 882L, 883L, 884L, 885L, 886L, 944L, 945L, 
946L, 947L, 948L, 949L, 950L, 951L, 952L, 953L, 954L, 955L, 956L, 
957L, 958L, 959L, 960L, 961L, 962L, 963L, 964L, 965L, 966L, 967L, 
968L, 969L, 970L, 971L, 972L, 973L, 974L, 975L, 976L, 977L, 978L, 
979L, 980L, 981L, 982L, 983L, 984L, 985L, 986L, 987L, 988L, 989L, 
990L, 991L, 992L, 993L, 994L, 995L, 996L, 997L, 998L, 999L, 1000L, 
1001L, 1002L, 1003L, 1004L, 1005L, 1006L, 1007L, 1008L, 1009L, 
1010L, 1011L, 1012L, 1013L, 1014L, 1015L, 1016L, 1017L, 1018L, 
1019L, 1020L, 1021L, 1022L, 1023L, 1024L, 1025L, 1026L, 1027L, 
1028L, 1029L, 1030L, 1031L, 1032L, 1033L, 1034L, 1035L, 1036L, 
1037L, 1038L, 1039L, 1040L, 1041L, 1042L, 1043L, 1044L, 1045L, 
1046L, 1047L, 1048L, 1049L, 1050L, 1051L, 1052L, 1053L, 1054L, 
1055L, 1056L, 1057L, 1058L, 1059L, 1060L, 1061L, 1062L, 1063L, 
1064L, 1065L, 1066L, 1067L, 1068L, 1069L, 1070L, 1071L, 1072L, 
1073L, 1074L, 1075L, 1076L, 1077L, 1078L, 1079L, 1080L, 1081L, 
1082L, 1083L, 1084L, 1085L, 1086L, 1087L, 1088L, 1089L, 1090L, 
1091L, 1092L, 1093L, 1094L, 1095L, 1096L, 1097L, 1098L, 1099L, 
1100L, 1101L, 1102L, 1103L, 1104L, 1105L, 1106L, 1107L, 1108L, 
1109L, 1110L, 1111L, 1112L, 1113L, 1114L, 1115L, 1116L, 1117L, 
1118L, 1119L, 1120L, 1121L, 1122L, 1123L, 1124L, 1125L, 1126L, 
1127L, 1128L, 1129L, 1130L, 1131L, 1132L, 1133L, 1134L, 1135L, 
1136L, 1137L, 1138L, 1139L, 1140L, 1141L, 1142L, 1143L, 1144L, 
1145L, 1146L, 1147L, 1148L, 1149L, 1150L, 1151L, 1152L, 1153L, 
1154L, 1155L, 1156L, 1157L, 1158L, 1159L, 1160L, 1161L, 1162L, 
1163L, 1164L, 1165L, 1166L, 1167L, 1168L, 1169L, 1170L, 1171L, 
1172L, 1173L, 1174L, 1175L, 1176L, 1177L, 1178L, 1179L, 1180L, 
1181L, 1182L, 1183L, 1184L, 1185L, 1186L, 1187L, 1188L, 1189L, 
1190L, 1191L, 1192L, 1193L, 1194L, 1195L, 1196L, 1197L, 1198L, 
1199L, 1200L, 1201L, 1202L, 1203L, 1204L, 1205L, 1206L, 1207L, 
1208L, 1209L, 1210L, 1211L, 1212L, 1213L, 1214L, 1215L, 1216L, 
1217L, 1218L, 1219L, 1220L, 1221L, 1222L, 1223L, 1224L, 1225L, 
1226L, 1227L, 1228L, 1229L, 1230L, 1231L, 1232L, 1233L, 1234L, 
1235L, 1236L, 1237L, 1238L, 1239L, 1240L, 1241L, 1242L, 1243L, 
1244L, 1245L, 1246L, 1247L, 1248L, 1249L, 1250L, 1251L, 1252L, 
1253L, 1254L))

Then using ggplot2 package together with logarithmic transformation $ln(x + 1)$ you can draw violin-plot and show quantiles:

library(ggplot2)
ggplot(df, aes(x = factor(Sex), y = log(Intensity + 1))) +
  geom_violin(draw_quantiles = c(.25, .5, .75, .95))

The result is:

Solved – the basis for the Box and Whisker Plot definition of an outlier

Boxplots

Here is a relevant section from Hoaglin, Mosteller and Tukey (2000): Understanding Robust and Exploratory Data Analysis. Wiley. Chapter 3, "Boxplots and Batch Comparison", written by John D. Emerson and Judith Strenio (from page 62):

[...] Our definition of outliers as data values that are smaller than $F_{L}-\frac{3}{2}d_{F}$ or larger than $F_{U}+\frac{3}{2}d_{F}$ is somewhat arbitrary, but experience with many data sets indicates that this definition serves well in identifying values that may require special attention.[...]

$F_{L}$ and $F_{U}$ denote the first and third quartile, whereas $d_{F}$ is the interquartile range (i.e. $F_{U}-F_{L}$).

They go on and show the application to a Gaussian population (page 63):

Consider the standard Gaussian distribution, with mean $0$ and variance $1$. We look for population values of this distribution that are analogous to the sample values used in the boxplot. For a symmetric distribution, the median equals the mean, so the population median of the standard Gaussian distribution is $0$. The population fourths are $-0.6745$ and $0.6745$, so the population fourth-spread is $1.349$, or about $\frac{4}{3}$. Thus $\frac{3}{2}$ times the fourth-spread is $2.0235$ (about $2$). The population outlier cutoffs are $\pm 2.698$ (about $2\frac{2}{3}$), and they contain $99.3\%$ of the distribution. [...]

[they] show that if the cutoffs are applied to a Gaussian distribution, then $0.7\%$ of the population is outside the outlier cutoffs; this figure provides a standard of comparison for judging the placement of the outlier cutoffs [...].

Further, they write

[...] Thus we can judge whether our data seem heavier-tailed than Gaussian by how many points fall beyond the outlier cutoffs. [...]

They provide a table with the expected proportion of values that fall outside the outlier cutoffs (labelled "Total % Out"):

So these cutoffs where never intended to be a strict rule about what data points are outliers or not. As you noted, even a perfect Normal distribution is expected to exhibit "outliers" in a boxplot.

Outliers

As far as I know, there is no universally accepted definition of outlier. I like the definition by Hawkins (1980):

An outlier is an observation which deviates so much from the other observations as to arouse suspicions that it was generated by a different mechanism.

Ideally, you should only treat data points as outliers once you understand why they don't belong to the rest of the data. A simple rule is not sufficient. A good treatment of outliers can be found in Aggarwal (2013).

References

Aggarwal CC (2013): Outlier Analysis. Springer.
Hawkins D (1980): Identification of Outliers. Chapman and Hall.
Hoaglin, Mosteller and Tukey (2000): Understanding Robust and Exploratory Data Analysis. Wiley.