How can I indicate the frequency of outliers of boxplots in ggplot?

Question

I have the following boxplots:

They have been generated with this code:

my_xlab <- paste(levels(adpt_info$age_class),"
(N=",table(adpt_info$age_class),")",sep="")
ggplot(adpt_info, aes(x=age_class, y=nr_trips)) + 
  geom_boxplot(varwidth = TRUE, alpha=0.2)+
  scale_x_discrete(labels=my_xlab)+
  stat_summary(fun.data = "mean_cl_normal", 
               aes(shape="mean"), 
               size=4,
               colour = "red",
               geom="point") +
  scale_shape_manual("", values=c("mean"="x"))+
  theme_minimal()

As you can see, the boxplots have an alpha value, which ought to indicate how many of the outliers with the same value occur. The nr_trips are integer values.

What I'd like to do is to add either a legend of the alpha value to the plot, or indicate the occurrence in a different way. Like this, it doesn't show well enough the differences in the distribution in my opinion.

Thank you for your help!

Data excerpt:

structure(list(age_class = structure(c(4L, 6L, 3L, 6L, 5L, 3L, 
7L, 4L, 4L, 7L, 7L, 6L, 6L, 7L, 7L, 5L, 1L, 6L, 3L, 5L, 5L, 2L, 
4L, 4L, 3L, 5L, 1L, 8L, 7L, 9L, 9L, 4L, 4L, 3L, 2L, 6L, 2L, 1L, 
5L, 8L, 8L, 7L, 4L, 4L, 9L, 9L, 8L, 4L, 4L, 6L, 6L, 5L, 5L, 8L, 
4L, 6L, 7L, 5L, 1L, 1L, 5L, 4L, 5L, 4L, 3L, 3L, 4L, 4L, 7L, 7L, 
6L, 5L, 2L, 5L, 3L, 5L, 4L, 1L, 6L, 6L, 3L, 6L, 1L, 1L, 5L, 8L, 
4L, 4L, 6L, 7L, 3L, 2L, 6L, 2L, 3L, 3L, 4L, 1L, 2L, 2L, 6L, 5L, 
5L, 5L, 4L, 4L, 6L, 3L, 3L, 5L, 5L, 7L, 4L, 1L, 3L, 4L, 1L, 5L, 
6L, 5L, 4L, 4L, 4L, 5L, 5L, 6L, 5L, 7L, 3L, 2L, 7L, 4L, 5L, 4L, 
4L, 8L, 3L, 7L, 7L, 8L, 5L, 4L, 4L, 2L, 6L, 6L, 3L, 6L, 3L, 9L, 
4L, 9L, 7L, 6L, 7L, 6L, 7L, 3L, 3L, 6L, 6L, 7L, 6L, 5L, 8L, 10L, 
6L, 4L, 2L, 2L, 2L, 6L, 2L, 7L, 3L, 7L, 7L, 4L, 5L, 3L, 3L, 6L, 
3L, 8L, 5L, 3L, 3L, 6L, 6L, 4L, 7L, 2L, 3L, 5L, 5L, 7L, 8L, 6L, 
6L, 5L, 9L, 9L, 8L, 7L, 4L, 6L, 3L, 4L, 5L, 5L, 5L, 8L, 5L, 6L, 
7L, 5L, 2L, 4L, 7L, 3L, 5L, 4L, 5L, 5L, 8L, 8L, 7L, 3L, 6L, 4L, 
10L, 7L, 6L, 5L, 6L, 7L, 7L, 6L, 7L, 5L, 5L, 6L, 6L, 7L, 7L, 
5L, 7L, 5L, 5L, 4L, 6L, 7L, 3L, 6L, 6L, 3L, 6L, 4L, 6L, 9L, 6L, 
7L, 7L, 5L, 2L, 2L, 4L, 5L, 3L, 3L, 6L, 2L, 4L, 1L, 2L, 5L, 5L, 
4L, 2L, 5L, 4L, 6L, 3L, 7L, 7L, 1L, 5L, 5L, 8L, 3L, 5L, 7L, 2L, 
3L, 8L, 7L, 6L, 6L, 3L, 4L, 5L, 5L, 9L, 6L, 3L, 6L, 8L, 5L, 5L, 
2L, 5L, 5L, 2L, 6L, 5L, 5L, 5L, 5L, 4L, 1L, 8L, 5L, 6L, 5L, 2L, 
2L, 6L, 7L, 5L, 8L, 7L, 5L, 5L, 8L, 8L, 10L, 10L, 7L, 5L, 10L, 
5L, 4L, 1L, 4L, 8L, 5L, 5L, 8L, 5L, 8L, 5L, 1L, 5L, 1L, 5L, 5L, 
4L, 2L, 7L, 2L, 6L, 7L, 5L, 6L, 7L, 6L, 5L, 2L, 6L, 5L, 4L, 4L, 
5L, 5L, 2L, 6L, 5L, 5L, 1L, 5L, 1L, 6L, 1L, 7L, 7L, 5L, 8L, 6L, 
2L, 6L, 5L, 7L, 7L, 6L, 2L, 3L, 3L, 3L, 6L, 4L, 4L, 6L, 5L, 7L, 
5L, 2L, 7L, 2L, 4L, 4L, 5L, 2L, 2L, 2L, 7L, 2L, 3L, 5L, 5L, 3L, 
5L, 6L, 5L, 7L, 6L, 7L, 5L, 8L, 4L, 7L, 6L, 6L, 5L, 8L, 6L, 2L, 
5L, 5L, 2L, 6L, 4L, 7L, 5L, 3L, 4L, 4L, 4L, 6L, 4L, 4L, 8L, 8L, 
6L, 6L, 2L, 3L, 3L, 7L, 7L, 6L, 7L, 5L, 5L, 6L, 6L, 1L, 5L, 4L, 
5L, 5L, 5L, 6L, 5L, 6L, 8L, 5L, 7L, 3L, 6L, 2L, 5L, 4L, 5L, 5L, 
4L, 8L, 3L, 7L, 7L, 8L, 4L, 7L, 4L, 4L, 7L, 7L, 5L, 2L, 5L, 10L, 
5L, 5L, 2L, 2L, 9L, 6L, 2L, 7L, 6L, 4L, 8L, 7L, 3L, 6L, 8L, 8L, 
7L, 7L, 8L, 6L, 2L, 4L, 7L, 7L, 7L, 7L, 7L, 6L, 2L, 4L, 4L, 2L, 
6L, 2L, 3L, 5L, 7L, 3L, 3L, 4L, 5L, 7L, 5L, 2L, 5L, 6L, 6L, 3L, 
4L, 4L, 8L, 7L, 5L, 2L, 6L, 9L, 8L, 8L, 5L, 4L, 8L, 8L, 2L, 6L, 
2L, 3L, 6L, 9L, 5L, 9L, 5L, 1L, 5L, 4L, 5L, 8L, 7L, 7L, 1L, 7L, 
5L, 1L, 1L, 5L, 3L, 6L, 2L, 2L, 2L, 7L, 8L, 4L, 3L, 8L, 5L, 6L, 
5L, 5L, 7L, 8L, 3L, 7L, 6L, 3L, 3L, 9L, 5L, 5L, 1L, 8L, 5L, 6L, 
3L, 1L, 3L, 3L, 6L, 3L, 6L, 9L, 4L, 10L, 10L, 8L, 5L, 5L, 5L, 
5L, 2L, 5L, 3L, 5L, 5L, 6L, 6L, 5L, 3L, 3L, 7L, 7L, 5L, 4L, 7L, 
4L, 7L, 4L, 4L, 6L, 6L, 7L, 4L, 5L, 5L, 2L, 2L, 1L, 7L, 2L, 5L, 
2L, 7L, 7L, 6L, 7L, 7L, 7L, 7L, 8L, 2L, 8L, 4L, 7L, 4L, 3L, 8L, 
2L, 6L, 3L, 6L, 3L, 5L, 4L, 5L, 6L, 3L, 4L, 4L, 5L, 2L, 5L, 2L, 
2L, 5L, 5L, 6L, 6L, 8L, 7L, 7L, 5L, 6L, 7L, 6L, 6L, 4L, 4L, 8L, 
4L, 2L, 5L, 2L, 5L, 6L, 6L, 5L, 5L, 2L, 5L, 9L, 8L, 7L, 5L, 7L, 
5L, 6L, 7L, 8L, 4L, 3L, 8L, 3L, 5L, 5L, 4L, 8L, 4L, 3L, 8L, 7L, 
6L, 4L, 6L, 8L, 5L, 6L, 5L, 7L, 5L, 6L, 4L, 6L, 8L, 8L, 6L, 7L, 
4L, 4L, 4L, 5L, 4L, 8L, 4L, 5L, 4L, 5L, 2L, 3L, 2L, 2L, 5L, 5L, 
2L, 2L, 5L, 5L, 2L, 6L, 5L, 5L, 5L, 6L, 4L, 7L, 5L, 3L, 5L, 2L, 
4L, 4L, 4L, 6L, 3L, 4L, 5L, 5L, 6L, 4L, 3L, 4L, 5L, 6L, 4L, 5L, 
3L, 3L, 1L, 6L, 2L, 3L, 4L, 5L, 6L, 3L, 3L, 4L, 3L, 5L, 4L, 3L, 
4L, 8L, 3L, 3L, 3L, 4L, 7L, 5L, 5L, 5L, 6L, 4L, 4L, 4L, 6L, 2L, 
1L, 4L, 6L, 4L, 4L, 5L, 2L, 4L, 4L, 4L, 4L, 4L, 3L, 3L, 5L, 2L, 
5L, 5L, 3L, 2L, 5L, 5L, 5L, 2L, 2L, 2L, 4L, 2L, 6L, 6L, 2L, 2L, 
5L, 4L, 4L, 4L, 3L, 5L, 3L, 6L, 3L, 3L, 6L, 3L, 5L, 1L, 5L, 4L, 
1L, 5L, 5L, 4L, 4L, 5L, 4L, 7L, 6L, 3L, 5L, 3L, 5L, 4L, 7L, 7L, 
2L, 6L, 2L, 4L, 6L, 1L, 3L, 2L, 5L, 5L, 5L, 2L, 2L, 4L, 2L, 3L, 
5L, 5L, 2L, 3L, 5L, 5L, 4L, 6L, 6L, 6L, 3L, 5L, 5L, 5L, 7L, 5L, 
6L, 3L, 6L, 4L, 6L, 4L, 3L, 5L, 3L, 7L, 7L, 1L, 4L, 5L, 6L, 5L, 
3L, 5L, 4L, 4L, 6L, 6L, 6L, 5L, 5L, 5L, 7L, 5L, 4L, 4L, 5L, 7L, 
7L, 9L, 3L, 7L, 3L, 5L, 4L, 6L, 5L, 3L, 7L, 6L, 4L, 6L, 7L, 4L, 
7L, 5L, 6L, 5L, 4L, 4L, 5L, 1L, 6L, 5L, 4L, 6L, 5L, 6L, 6L, 5L, 
3L, 6L, 6L, 4L, 4L, 3L, 4L, 5L, 6L, 4L, 6L, 3L, 6L, 3L, 4L, 5L, 
4L, 4L, 6L, 6L, 3L, 5L, 3L, 5L, 1L, 5L, 8L, 6L, 4L, 6L, 5L, 4L, 
2L, 1L, 5L, 5L, 2L, 2L, 4L, 1L, 6L, 7L, 8L, 2L, 5L, 7L, 7L, 3L, 
9L, 3L, 6L, 7L, 5L, 3L, 6L, 3L, 7L, 9L, 8L, 8L, 3L, 5L, 5L, 8L, 
4L, 4L, 4L, 2L, 2L, 3L, 5L, 5L, 3L, 3L, 4L, 4L, 9L, 4L, 1L, 4L, 
4L, 2L, 5L, 9L, 7L, 3L, 4L, 1L, 4L, 1L, 4L, 4L, 6L, 7L, 9L, 6L, 
6L, 5L, 4L, 6L, 4L, 3L, 4L, 9L, 9L, 5L, 7L, 6L, 7L, 2L, 2L, 6L, 
4L, 5L, 6L, 7L, 6L, 3L, 3L, 4L, 8L, 9L, 6L, 4L, 8L, 5L, 6L, 4L, 
5L, 5L, 2L, 6L, 7L, 5L, 2L, 4L, 5L, 4L, 1L, 9L, 4L, 7L, 2L, 6L, 
5L, 4L, 1L, 4L, 1L, 4L, 6L, 3L, 6L, 7L, 4L, 6L, 4L, 5L, 1L, 4L, 
4L, 5L, 6L, 6L, 6L, 4L, 8L, 5L, 5L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 
6L, 4L, 4L, 4L, 3L, 4L, 5L, 1L, 6L, 7L, 5L, 1L, 2L, 6L, 8L, 8L, 
4L, 3L, 3L, 6L, 4L, 5L, 4L, 2L, 4L, 7L, 7L, 4L, 7L, 5L, 4L, 7L, 
8L, 3L, 9L, 2L, 5L, 5L, 2L, 3L, 7L, 4L, 7L, 7L, 4L, 6L, 4L, 4L, 
4L, 7L, 4L, 10L, 5L, 5L, 5L, 4L, 5L, 3L, 6L, 4L, 6L, 9L, 7L, 
5L, 5L, 6L, 4L, 8L, 6L, 3L, 3L, 4L, 7L, 6L, 7L, 8L, 4L, 6L, 7L, 
3L, 8L, 8L, 7L, 3L, 3L, 5L, 4L, 5L, 5L, 4L, 3L, 4L, 5L, 4L, 5L, 
1L, 4L, 4L, 4L, 7L, 6L, 3L, 7L, 4L, 2L, 9L, 9L, 8L, 2L, 3L, 6L, 
8L, 7L, 7L, 1L, 4L, 7L, 5L, 6L, 4L, 6L, 8L, 6L, 5L, 6L, 5L, 3L, 
4L, 4L, 2L, 7L, 3L, 6L, 6L, 3L, 5L, 6L, 4L, 4L, 6L, 8L, 5L, 1L, 
3L, 4L, 5L, 5L, 3L, 6L, 2L, 5L, 3L, 4L, 3L, 6L, 1L, 4L, 2L, 4L, 
3L, 4L, 3L, 4L, 2L, 4L, 2L, 6L, 4L, 6L, 2L, 7L, 3L, 5L, 2L, 5L, 
6L, 7L, 7L, 1L, 3L, 7L, 4L, 4L, 4L, 7L, 3L, 7L, 2L, 4L, 4L, 5L, 
3L, 4L, 7L, 2L, 2L, 2L, 5L, 5L, 4L, 4L, 3L, 8L, 8L, 6L, 5L, 7L, 
7L, 6L, 5L, 9L, 6L, 2L, 2L, 3L, 8L, 5L, 7L, 5L, 5L, 6L, 1L, 2L, 
5L, 4L, 5L, 2L, 5L, 4L, 4L, 6L, 6L, 4L, 2L, 5L, 7L, 4L, 1L, 4L, 
4L, 4L, 3L, 5L, 3L, 4L, 5L, 5L, 6L, 4L, 4L, 5L, 2L, 4L, 1L, 8L, 
8L, 8L, 6L, 4L, 4L, 4L, 8L, 4L, 9L, 5L, 5L, 5L, 9L, 5L, 3L, 6L, 
6L, 6L, 5L, 4L, 3L, 4L, 7L, 9L, 7L, 4L, 4L, 4L, 3L, 1L, 4L, 5L, 
5L, 5L, 1L, 6L, 2L, 3L, 5L, 3L, 4L, 5L, 5L, 2L, 7L, 6L, 2L, 5L, 
4L, 8L, 3L, 5L, 4L, 6L, 5L, 4L, 5L, 5L, 7L, 5L, 4L, 4L, 4L, 7L, 
6L, 3L, 3L, 5L, 4L, 2L, 2L, 5L, 2L, 5L, 1L, 4L, 4L, 5L, 3L, 5L, 
7L, 7L, 4L, 4L, 6L, 5L, 7L, 4L, 6L, 7L, 5L, 3L, 7L, 1L, 6L, 2L, 
3L, 3L, 3L, 3L, 4L, 4L, 4L, 8L, 5L, 3L, 6L, 9L, 6L, 6L, 4L, 9L, 
3L, 4L, 7L, 4L, 1L, 4L, 7L, 3L, 5L, 5L, 4L, 6L, 9L, 8L, 4L, 4L, 
6L, 3L, 3L, 8L, 9L, 5L, 2L, 5L, 2L, 5L, 4L, 8L, 2L, 9L, 6L, 3L, 
6L, 5L, 2L, 7L, 4L, 8L, 8L, 7L, 8L, 2L, 2L, 5L, 2L, 2L, 3L, 2L, 
6L, 8L, 9L, 3L, 5L, 6L, 7L, 6L, 4L, 8L, 2L, 8L, 5L, 2L, 4L, 4L, 
5L, 7L, 2L, 2L, 6L, 3L, 1L, 6L, 4L, 6L, 4L, 4L, 3L, 3L, 4L, 1L, 
4L, 9L, 6L, 3L, 3L, 2L, 5L, 2L, 5L, 1L, 6L, 3L, 2L, 8L, 3L, 6L, 
2L, 5L, 2L, 5L, 5L, 7L, 3L, 4L, 1L, 2L, 9L, 4L, 3L, 3L, 6L, 1L, 
2L, 6L, 3L, 7L, 3L, 6L, 7L, 7L, 9L, 4L, 6L, 4L, 1L, 3L, 4L, 6L, 
2L, 5L, 6L, 6L, 4L, 5L, 2L, 6L, 8L, 8L, 8L, 2L, 6L, 2L, 5L, 4L, 
6L, 3L, 5L, 7L, 3L, 4L, 5L, 9L, 8L, 8L, 4L, 6L, 4L, 3L, 5L, 3L, 
3L, 4L, 9L, 4L, 4L, 2L, 2L, 5L, 2L, 3L, 8L, 8L, 3L, 5L, 1L, 6L, 
9L, 4L, 3L, 4L, 3L, 8L, 7L, 4L, 5L, 6L, 5L, 4L, 2L, 8L, 6L, 5L, 
5L, 6L, 3L, 5L, 6L, 3L, 6L, 2L, 4L, 4L, 5L, 4L, 1L, 5L, 5L, 1L, 
7L, 6L, 3L, 7L, 4L, 6L, 3L, 6L, 6L, 7L, 4L, 6L, 5L, 6L, 5L, 5L, 
2L, 4L, 5L, 6L, 3L, 5L, 3L, 3L, 6L, 6L, 5L, 5L, 3L, 4L, 9L, 1L, 
2L, 4L, 5L, 3L, 4L, 4L, 3L, 6L, 2L, 4L, 4L, 6L, 5L, 6L, 6L, 3L, 
3L, 7L, 6L, 6L, 7L, 6L, 3L, 5L, 2L, 5L, 7L, 9L, 1L, 8L, 8L, 6L, 
9L, 5L, 4L, 1L, 2L, 7L, 6L, 8L, 5L, 3L, 3L, 6L, 7L, 7L, 5L, 3L, 
3L, 4L, 5L, 1L, 5L, 6L, 5L, 7L, 5L, 8L, 4L, 3L, 8L, 4L, 5L, 3L, 
5L, 4L, 4L, 6L, 4L, 9L, 6L, 6L, 3L, 6L, 8L, 6L, 5L, 6L, 6L, 4L, 
6L, 5L, 4L, 8L, 8L, 5L, 5L, 3L, 2L, 5L, 8L, 3L, 7L, 6L, 4L, 3L, 
6L, 5L, 5L, 7L, 4L, 5L, 6L, 8L, 5L, 6L, 4L, 4L, 9L, 6L, 5L, 8L, 
5L, 5L, 6L, 2L, 5L, 7L, 5L, 4L, 9L, 7L, 5L, 9L, 5L, 4L, 3L, 7L, 
6L, 7L, 6L, 3L, 4L, 6L, 8L, 5L, 6L, 2L, 3L, 4L, 4L, 7L, 4L, 4L, 
7L, 6L, 4L, 8L, 8L, 5L, 4L, 5L, 3L, 3L, 6L, 6L, 8L, 3L, 5L, 4L, 
3L, 5L, 6L, 8L, 4L, 6L, 6L, 6L, 7L, 5L, 3L, 5L, 8L, 7L, 5L, 6L, 
3L, 5L, 5L, 5L, 6L, 5L, 4L, 7L, 8L, 10L, 8L, 7L, 8L, 3L, 9L, 
3L, 8L, 3L, 3L, 4L, 7L, 4L, 3L, 2L, 3L, 6L, 5L, 6L, 6L, 3L, 4L, 
4L, 3L, 7L, 2L, 4L, 4L, 2L, 5L, 1L, 4L, 6L, 7L, 2L, 2L, 2L, 3L, 
3L, 2L, 3L, 6L, 6L, 4L, 4L, 3L, 5L, 3L, 5L, 4L, 2L, 5L, 2L, 4L, 
6L, 4L, 3L, 4L, 3L, 7L, 6L, 6L, 5L, 5L, 3L, 4L, 4L, 4L, 6L, 2L, 
3L, 1L, 5L, 5L, 6L, 6L, 2L, 8L, 8L, 4L, 3L, 8L, 5L, 2L, 4L, 4L, 
3L, 5L, 6L, 6L, 3L, 2L, 2L, 4L, 4L, 5L, 5L, 2L, 7L, 7L, 4L, 4L, 
4L, 3L, 2L, 5L, 4L, 4L, 6L, 9L, 7L, 9L, 6L, 2L, 3L, 5L, 8L, 7L, 
6L, 6L, 3L, 4L, 1L, 8L, 6L, 3L, 3L, 2L, 5L, 4L, 4L, 3L, 1L, 4L, 
4L, 7L, 2L, 5L, 5L, 3L, 4L, 4L, 3L, 4L, 4L, 7L, 4L, 4L, 6L, 4L, 
6L, 1L, 4L, 6L, 5L, 3L, 6L, 3L, 6L, 6L, 5L, 2L, 1L, 3L, 2L, 4L, 
5L, 3L, 6L, 2L, 5L, 4L, 3L, 3L, 6L, 3L, 6L, 4L, 3L, 5L, 3L, 4L, 
3L, 5L, 2L, 4L, 3L, 7L, 6L, 4L, 3L, 2L, 5L, 4L, 4L, 5L, 3L, 4L, 
4L, 4L, 4L, 4L, 3L, 7L, 5L, 4L, 3L, 5L, 7L, 9L, 5L, 7L, 1L, 6L, 
5L, 3L, 2L, 5L, 8L, 6L, 3L, 2L, 3L, 4L, 4L, 4L, 7L, 7L, 5L, 3L, 
2L, 10L, 3L, 3L, 3L, 7L, 7L, 7L, 5L, 4L, 8L, 9L, 3L, 4L, 4L, 
4L, 7L, 3L, 4L, 7L, 7L, 5L, 6L, 8L, 7L, 5L, 4L, 2L, 5L, 3L, 3L, 
2L, 5L, 5L, 1L, 8L, 3L, 4L, 9L, 6L, 7L, 3L, 2L, 5L, 6L, 6L, 8L, 
5L, 5L, 6L, 6L, 3L, 4L, 4L, 5L, 3L, 5L, 6L, 6L, 4L, 2L, 6L, 4L, 
2L, 3L, 2L, 2L, 5L, 7L, 3L, 3L, 3L, 3L, 3L, 2L, 3L, 3L, 3L, 5L, 
6L, 5L, 3L, 7L, 6L, 4L, 4L, 5L, 7L, 2L, 2L, 4L, 4L, 4L, 1L, 7L, 
7L, 3L, 2L, 4L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 3L, 4L, 5L, 6L, 2L, 
2L, 5L, 2L, 2L, 7L, 4L, 4L, 4L, 6L, 6L, 5L, 4L, 8L, 8L, 7L, 6L, 
7L, 5L, 4L, 3L, 7L, 1L, 4L, 5L, 5L, 3L, 2L, 1L, 4L, 1L, 6L, 3L, 
4L, 8L, 5L, 6L, 4L, 6L, 1L, 5L, 3L, 5L, 5L, 2L, 7L, 7L, 3L, 3L, 
6L, 5L, 1L, 5L, 4L, 4L, 7L, 4L, 4L, 3L, 5L, 8L, 4L, 2L, 4L, 2L, 
5L, 8L, 6L, 3L, 6L, 3L, 4L, 3L, 7L, 4L, 8L, 5L, 5L, 1L, 5L, 2L, 
3L, 4L, 8L, 6L, 6L, 2L, 8L, 7L, 6L, 4L, 6L, 8L, 6L, 6L, 6L, 5L, 
3L, 8L, 4L, 5L, 4L, 5L, 3L, 3L, 5L, 4L, 5L, 5L, 5L, 7L, 7L, 7L, 
6L, 4L, 4L, 7L, 4L, 4L, 4L, 3L, 2L, 3L, 5L, 3L, 3L, 5L, 2L, 1L, 
5L, 5L, 5L, 5L, 3L, 5L, 5L, 5L, 5L, 2L, 5L, 7L, 9L, 4L, 5L, 4L, 
4L, 4L, 5L, 2L, 2L, 5L, 7L, 3L, 3L, 2L, 3L, 7L, 7L, 6L, 3L, 2L, 
2L, 3L, 2L, 5L, 6L, 6L, 4L, 7L, 3L, 4L, 4L, 3L, 4L, 5L, 6L, 6L, 
3L, 3L, 3L, 6L, 2L, 5L, 5L, 3L, 5L, 7L, 6L, 8L, 4L, 3L, 2L, 3L, 
8L, 3L, 4L, 4L, 5L, 3L, 8L, 4L, 7L, 5L, 7L, 5L, 4L, 4L, 9L, 7L, 
4L, 6L, 6L, 4L, 4L, 4L, 3L, 3L, 4L, 7L, 7L, 3L, 6L, 3L, 2L, 5L, 
4L, 5L, 2L, 4L, 7L, 6L, 8L, 3L, 5L, 5L, 3L, 3L, 2L, 7L, 5L, 2L, 
4L, 8L, 8L, 5L, 3L, 4L, 7L, 8L, 4L, 8L, 4L, 3L, 6L, 3L, 5L, 4L, 
5L, 7L, 3L, 3L, 7L, 7L, 3L, 5L, 10L, 7L, 7L, 4L, 5L, 7L, 2L, 
9L, 6L, 4L, 4L, 3L, 4L, 3L, 5L, 4L, 5L, 4L, 8L, 6L, 3L, 4L, 9L, 
3L, 4L, 6L, 4L, 4L, 4L, 7L, 7L, 6L, 5L, 8L, 3L, 7L, 3L, 4L, 6L, 
2L, 2L, 6L, 4L, 5L, 6L, 3L, 4L, 9L, 6L, 4L, 4L, 7L, 7L, 5L, 7L, 
7L, 6L, 6L, 6L, 4L, 5L, 4L, 3L, 7L, 6L, 6L, 6L, 3L, 3L, 7L, 5L, 
4L, 5L, 8L, 5L, 4L, 6L, 3L, 8L, 5L, 4L, 4L, 4L, 7L, 9L, 4L, 8L, 
3L, 4L, 3L, 6L, 5L, 1L, 4L, 9L, 5L, 4L, 6L, 3L, 3L, 6L, 5L, 6L, 
7L, 7L, 7L, 7L, 3L, 8L, 5L, 8L, 4L, 6L, 5L, 3L, 7L, 4L, 7L, 6L, 
5L, 6L, 8L, 9L, 6L, 7L, 4L, 4L, 6L, 4L, 4L, 8L, 4L, 8L, 6L, 6L, 
4L, 3L, 7L, 4L, 9L, 4L, 3L, 7L, 9L, 4L, 5L, 2L, 3L, 3L, 6L, 3L, 
5L, 2L, 6L, 2L, 10L, 5L, 3L, 4L, 6L, 3L, 3L, 6L, 8L, 4L, 4L, 
2L, 5L, 3L, 3L, 5L, 6L, 4L, 6L, 6L, 4L, 2L, 2L, 2L, 6L, 2L, 3L, 
1L, 3L, 3L, 7L, 1L, 2L, 7L, 4L, 6L, 4L, 1L, 6L, 4L, 4L, 4L, 5L, 
5L, 8L, 5L, 2L, 2L, 4L, 5L, 5L, 8L, 6L, 4L, 3L, 5L, 3L, 7L, 7L, 
9L, 1L, 5L, 5L, 4L, 5L, 1L, 7L, 4L, 4L, 5L, 1L, 5L, 2L, 6L, 3L, 
5L, 6L, 4L, 6L, 6L, 3L, 3L, 5L, 4L, 3L, 6L, 6L, 7L, 3L, 3L, 3L, 
5L, 3L, 5L, 7L, 3L, 6L, 6L, 8L, 4L, 1L, 4L, 7L, 1L, 6L, 2L, 2L, 
6L, 2L, 6L, 5L, 2L, 7L, 2L, 6L, 2L, 5L, 6L, 3L, 3L, 1L, 3L, 4L, 
4L, 1L, 5L, 8L, 5L, 4L, 4L, 3L, 3L, 6L, 6L, 6L, 4L, 2L, 2L, 7L, 
8L, 3L, 8L, 4L, 8L, 4L, 4L, 7L, 2L, 5L, 4L, 2L, 1L, 5L, 4L, 2L, 
1L, 1L, 4L, 2L, 6L, 5L, 7L, 6L, 4L, 4L, 5L, 4L, 2L, 2L, 6L, 2L, 
4L, 4L, 3L, 3L, 4L, 6L, 5L, 2L, 7L, 7L, 7L, 3L, 9L, 8L, 5L, 5L, 
5L, 2L, 3L, 7L, 5L, 2L, 5L, 5L, 2L, 4L, 6L, 5L, 2L, 8L, 5L, 6L, 
3L, 4L, 4L, 4L, 5L, 6L, 6L, 7L, 4L, 5L, 2L, 3L, 2L, 3L, 3L, 4L, 
4L, 6L, 8L, 7L, 1L, 4L, 4L, 5L, 5L, 2L, 5L, 3L, 3L, 5L, 2L, 5L, 
6L, 6L, 5L, 5L, 9L, 2L, 6L, 6L, 4L, 4L, 5L, 4L, 4L, 5L, 7L, 5L, 
4L, 8L, 3L, 6L, 3L, 7L, 2L, 2L, 5L, 3L, 6L, 6L, 1L, 4L, 4L, 3L, 
6L, 6L, 4L, 8L, 5L, 5L, 4L, 1L, 2L, 4L), .Label = c("10", "20", 
"30", "40", "50", "60", "70", "80", "90", "100", "110"), class = "factor"), 
    nr_trips = c(2, 2, 3, 3, 4, 2, 2, 2, 2, 3, 3, 3, 6, 5, 4, 
    3, 4, 3, 3, 3, 4, 3, 3, 2, 3, 3, 2, 3, 3, 4, 3, 3, 4, 3, 
    5, 7, 2, 3, 3, 3, 3, 6, 3, 7, 2, 2, 2, 3, 8, 3, 4, 3, 3, 
    4, 2, 3, 4, 3, 2, 2, 4, 4, 4, 3, 3, 3, 2, 5, 4, 4, 3, 3, 
    5, 5, 3, 3, 3, 3, 3, 4, 3, 3, 2, 3, 4, 3, 7, 4, 4, 2, 3, 
    3, 3, 2, 5, 3, 3, 2, 3, 5, 3, 3, 4, 3, 2, 5, 2, 5, 7, 3, 
    6, 3, 5, 2, 8, 4, 3, 3, 2, 3, 2, 3, 3, 5, 3, 3, 7, 3, 2, 
    4, 3, 3, 3, 6, 4, 2, 3, 3, 4, 2, 3, 3, 4, 2, 4, 4, 4, 4, 
    4, 2, 4, 3, 4, 5, 2, 5, 2, 3, 4, 2, 5, 5, 3, 5, 4, 3, 3, 
    2, 2, 3, 4, 4, 2, 2, 6, 2, 2, 2, 5, 3, 2, 2, 2, 3, 3, 2, 
    2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 2, 5, 2, 4, 2, 6, 4, 2, 4, 
    3, 2, 4, 3, 3, 3, 2, 5, 2, 3, 2, 3, 3, 3, 3, 3, 3, 2, 2, 
    4, 3, 3, 3, 2, 3, 3, 4, 2, 9, 5, 2, 3, 4, 3, 5, 3, 3, 3, 
    2, 6, 3, 3, 2, 2, 2, 2, 3, 2, 4, 2, 4, 4, 3, 4, 2, 2, 2, 
    2, 3, 3, 4, 3, 2, 3, 2, 7, 2, 3, 3, 3, 5, 3, 3, 4, 3, 4, 
    3, 2, 3, 5, 2, 4, 3, 2, 2, 3, 8, 2, 3, 3, 3, 3, 2, 2, 3, 
    3, 3, 2, 3, 2, 3, 2, 2, 5, 3, 2, 5, 2, 4, 5, 5, 4, 3, 4, 
    2, 5, 4, 4, 2, 2, 4, 2, 4, 2, 3, 3, 7, 4, 2, 3, 2, 4, 3, 
    5, 2, 3, 2, 2, 4, 4, 7, 4, 3, 3, 4, 5, 2, 2, 2, 5, 3, 4, 
    3, 3, 4, 7, 5, 3, 5, 5, 3, 2, 5, 3, 3, 4, 3, 3, 3, 2, 2, 
    3, 5, 4, 3, 2, 5, 4, 3, 2, 2, 5, 3, 2, 3, 3, 5, 4, 2, 4, 
    3, 2, 5, 5, 5, 6, 5, 3, 3, 2, 2, 3, 2, 2, 3, 4, 5, 2, 2, 
    4, 4, 4, 4, 7, 2, 2, 3, 3, 3, 4, 4, 3, 3, 2, 4, 4, 3, 5, 
    4, 2, 4, 3, 2, 2, 3, 3, 3, 5, 2, 2, 4, 3, 3, 5, 3, 3, 2, 
    3, 6, 3, 5, 2, 3, 5, 3, 5, 3, 2, 2, 3, 2, 3, 5, 3, 3, 2, 
    3, 4, 2, 4, 3, 3, 4, 3, 3, 3, 3, 5, 2, 3, 3, 2, 2, 5, 3, 
    3, 3, 5, 4, 3, 3, 2, 5, 3, 3, 5, 4, 3, 3, 3, 3, 3, 3, 4, 
    3, 2, 3, 5, 4, 5, 2, 3, 3, 2, 5, 2, 3, 5, 4, 2, 4, 6, 5, 
    2, 3, 3, 2, 4, 5, 4, 2, 4, 3, 6, 3, 3, 2, 3, 3, 2, 6, 2, 
    4, 2, 3, 5, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3, 5, 2, 2, 4, 4, 
    9, 2, 4, 2, 3, 3, 4, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 5, 2, 
    4, 3, 3, 8, 2, 4, 4, 3, 5, 4, 6, 2, 4, 2, 3, 4, 3, 2, 4, 
    6, 2, 4, 3, 3, 2, 2, 3, 6, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 
    2, 5, 3, 2, 5, 2, 5, 3, 2, 6, 2, 5, 2, 3, 4, 4, 2, 3, 2, 
    3, 2, 2, 4, 3, 6, 4, 3, 7, 3, 6, 4, 2, 3, 6, 3, 3, 3, 3, 
    3, 2, 3, 4, 3, 3, 2, 3, 5, 3, 2, 2, 5, 5, 4, 4, 3, 3, 3, 
    2, 4, 6, 5, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 7, 4, 
    3, 3, 4, 2, 2, 4, 5, 3, 4, 2, 2, 4, 2, 4, 6, 4, 3, 3, 5, 
    3, 2, 7, 6, 3, 2, 2, 3, 2, 6, 2, 2, 3, 4, 3, 3, 3, 3, 2, 
    3, 5, 4, 2, 2, 3, 4, 5, 3, 3, 3, 3, 3, 5, 2, 3, 5, 5, 4, 
    3, 3, 2, 2, 3, 4, 2, 3, 2, 2, 4, 3, 3, 5, 4, 2, 3, 3, 3, 
    2, 3, 3, 2, 5, 2, 2, 2, 4, 2, 3, 3, 6, 4, 4, 2, 2, 2, 3, 
    3, 3, 2, 3, 2, 3, 3, 2, 4, 2, 5, 3, 3, 3, 3, 4, 2, 3, 3, 
    3, 3, 2, 3, 2, 5, 3, 2, 3, 3, 4, 3, 6, 3, 3, 2, 2, 2, 3, 
    3, 2, 2, 2, 7, 2, 3, 4, 5, 3, 5, 3, 3, 4, 4, 3, 2, 3, 2, 
    2, 3, 5, 2, 3, 5, 4, 3, 3, 6, 2, 5, 3, 3, 4, 3, 3, 4, 3, 
    3, 3, 2, 3, 2, 2, 4, 3, 3, 2, 2, 5, 4, 2, 4, 4, 5, 2, 3, 
    2, 3, 2, 3, 3, 5, 3, 3, 3, 6, 4, 6, 4, 6, 3, 2, 2, 2, 2, 
    2, 5, 3, 2, 2, 3, 3, 3, 3, 3, 6, 4, 2, 2, 3, 3, 2, 2, 2, 
    3, 2, 2, 2, 5, 3, 4, 4, 3, 2, 2, 3, 2, 3, 3, 2, 2, 3, 4, 
    3, 4, 2, 2, 4, 3, 4, 3, 2, 2, 3, 2, 2, 3, 3, 6, 3, 2, 3, 
    3, 2, 3, 2, 3, 2, 2, 3, 4, 3, 3, 2, 4, 4, 2, 3, 4, 3, 5, 
    3, 2, 2, 3, 3, 4, 2, 3, 4, 3, 2, 4, 2, 3, 4, 3, 3, 2, 2, 
    3, 4, 3, 2, 3, 2, 3, 2, 2, 4, 3, 3, 2, 2, 4, 3, 3, 3, 3, 
    2, 2, 3, 3, 2, 5, 2, 3, 2, 2, 4, 5, 4, 2, 3, 3, 4, 2, 2, 
    3, 2, 5, 2, 3, 2, 3, 5, 2, 2, 5, 2, 2, 2, 3, 3, 5, 3, 4, 
    4, 2, 3, 2, 2, 7, 2, 3, 4, 3, 2, 2, 4, 3, 2, 2, 2, 4, 2, 
    2, 3, 2, 3, 2, 5, 3, 4, 4, 2, 2, 4, 3, 4, 2, 2, 5, 3, 2, 
    3, 2, 3, 4, 3, 4, 2, 3, 2, 3, 3, 2, 2, 4, 5, 2, 3, 3, 2, 
    4, 4, 4, 2, 3, 3, 5, 2, 3, 2, 5, 3, 2, 2, 4, 3, 2, 4, 4, 
    3, 4, 6, 3, 3, 2, 6, 2, 2, 8, 3, 3, 3, 4, 3, 3, 6, 2, 3, 
    3, 3, 3, 2, 4, 3, 3, 5, 5, 6, 3, 7, 4, 3, 2, 7, 3, 3, 3, 
    3, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 5, 3, 3, 3, 5, 
    4, 3, 2, 3, 2, 5, 4, 3, 3, 4, 4, 2, 2, 3, 2, 3, 2, 2, 2, 
    2, 3, 4, 4, 3, 3, 3, 2, 4, 3, 2, 3, 4, 3, 2, 3, 2, 4, 5, 
    2, 2, 2, 3, 6, 6, 3, 2, 4, 3, 2, 2, 3, 4, 4, 3, 2, 4, 2, 
    2, 2, 3, 3, 3, 3, 3, 5, 2, 3, 5, 4, 4, 3, 3, 4, 4, 2, 6, 
    4, 3, 3, 3, 4, 2, 2, 2, 3, 3, 3, 6, 2, 2, 3, 5, 2, 5, 3, 
    2, 3, 3, 2, 2, 2, 2, 2, 3, 2, 3, 4, 2, 3, 3, 4, 4, 2, 3, 
    3, 2, 2, 3, 2, 2, 5, 3, 2, 3, 3, 3, 2, 2, 2, 4, 3, 2, 2, 
    2, 2, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
    3, 2, 3, 2, 2, 2, 3, 3, 2, 4, 2, 2, 2, 2, 3, 4, 3, 3, 3, 
    3, 2, 2, 2, 2, 3, 2, 4, 3, 3, 3, 4, 4, 3, 2, 2, 3, 5, 5, 
    4, 2, 2, 3, 2, 4, 3, 2, 2, 2, 5, 3, 4, 3, 5, 3, 4, 3, 2, 
    5, 7, 3, 3, 2, 3, 2, 5, 3, 5, 2, 2, 2, 4, 3, 3, 3, 3, 3, 
    5, 3, 6, 2, 3, 4, 6, 3, 2, 4, 3, 3, 2, 3, 6, 3, 4, 2, 4, 
    6, 7, 4, 3, 2, 3, 3, 4, 2, 2, 3, 2, 5, 2, 2, 2, 3, 3, 3, 
    2, 3, 2, 3, 2, 4, 2, 5, 2, 2, 4, 2, 3, 4, 4, 3, 3, 2, 4, 
    3, 2, 3, 3, 3, 3, 2, 6, 2, 3, 2, 2, 3, 3, 3, 3, 3, 4, 7, 
    3, 2, 3, 2, 2, 2, 3, 3, 3, 4, 3, 2, 3, 5, 3, 2, 5, 3, 4, 
    3, 3, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 3, 5, 3, 2, 3, 
    3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 4, 5, 4, 2, 5, 2, 3, 
    3, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 3, 2, 3, 3, 3, 5, 3, 
    2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 7, 2, 
    2, 4, 5, 2, 6, 3, 2, 2, 3, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2, 
    4, 2, 3, 3, 2, 3, 3, 5, 3, 2, 2, 5, 2, 4, 2, 3, 2, 4, 2, 
    3, 4, 2, 3, 3, 3, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3, 3, 4, 3, 
    3, 2, 3, 3, 5, 7, 5, 2, 4, 3, 4, 5, 3, 3, 3, 3, 2, 2, 3, 
    2, 2, 3, 4, 3, 4, 4, 4, 2, 5, 3, 3, 2, 2, 3, 4, 3, 2, 4, 
    3, 2, 3, 2, 2, 3, 3, 4, 3, 3, 3, 4, 6, 2, 4, 3, 2, 5, 3, 
    2, 3, 2, 2, 4, 2, 3, 2, 4, 3, 3, 3, 3, 3, 3, 4, 2, 3, 2, 
    5, 8, 2, 2, 3, 6, 3, 3, 3, 3, 2, 2, 2, 4, 2, 4, 3, 3, 2, 
    3, 2, 3, 4, 2, 3, 3, 4, 2, 3, 4, 4, 2, 2, 2, 4, 3, 3, 3, 
    4, 4, 4, 2, 3, 2, 3, 3, 2, 8, 3, 2, 3, 3, 3, 2, 3, 2, 3, 
    2, 3, 5, 4, 2, 2, 3, 10, 3, 4, 3, 2, 2, 3, 3, 2, 5, 3, 3, 
    3, 3, 4, 2, 3, 2, 3, 3, 3, 2, 2, 4, 2, 3, 2, 3, 3, 3, 3, 
    3, 3, 2, 3, 4, 2, 3, 2, 2, 2, 5, 2, 4, 2, 2, 3, 3, 3, 3, 
    3, 4, 5, 3, 2, 3, 5, 2, 4, 3, 3, 2, 3, 3, 4, 2, 3, 5, 2, 
    5, 3, 2, 3, 2, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 5, 3, 3, 4, 
    2, 3, 2, 3, 2, 4, 2, 2, 2, 3, 5, 3, 2, 4, 6, 4, 5, 2, 2, 
    2, 2, 2, 8, 2, 2, 3, 2, 3, 2, 3, 2, 3, 5, 2, 3, 2, 3, 4, 
    4, 2, 5, 6, 4, 5, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 3, 
    3, 2, 2, 4, 2, 5, 3, 4, 2, 2, 2, 2, 3, 3, 2, 5, 2, 4, 2, 
    2, 2, 4, 3, 3, 2, 5, 3, 2, 4, 3, 2, 2, 2, 4, 3, 4, 3, 2, 
    3, 2, 7, 4, 2, 3, 5, 3, 3, 3, 2, 3, 7, 2, 2, 3, 3, 3, 5, 
    2, 3, 3, 4, 3, 2, 3, 3, 4, 3, 2, 3, 3, 3, 6, 3, 2, 3, 2, 
    4, 3, 3, 2, 4, 3, 2, 3, 3, 2, 2, 6, 3, 2, 2, 2, 2, 3, 5, 
    2, 4, 3, 2, 4, 2, 4, 2, 3, 6, 2, 2, 3, 4, 2, 3, 3, 2, 2, 
    2, 2, 5, 2, 3, 3, 3, 3, 7, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 
    4, 4, 4, 5, 3, 3, 5, 3, 3, 5, 3, 3, 2, 2, 2, 5, 2, 4, 3, 
    2, 3, 3, 4, 3, 5, 3, 3, 3, 2, 3, 2, 4, 5, 2, 3, 3, 2, 2, 
    3, 2, 2, 3, 2, 3, 3, 2, 6, 2, 5, 2, 4, 5, 2, 3, 3, 5, 3, 
    2, 2, 4, 3, 3, 4, 4, 3, 2, 5, 3, 3, 2, 3, 7, 2, 4, 3, 2, 
    4, 5, 2, 3, 2, 2, 2, 3, 3, 4, 4, 3, 3, 3, 3, 4, 3, 3, 5, 
    3, 4, 2, 3, 5, 5, 3, 3, 4, 2, 3, 3, 2, 3, 2, 2, 2, 2, 5, 
    2, 4, 3, 2, 3, 2, 3, 3, 2, 4, 2, 4, 3, 3, 2, 2, 6, 2, 2, 
    2, 3, 2, 2, 2, 5, 2, 3, 2, 3, 2, 3, 5, 5, 2, 2, 5, 2, 3, 
    3, 3, 2, 4, 4, 2, 3, 2, 2, 4, 3, 5, 4, 3, 5, 5, 4, 2, 3, 
    3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 4, 4, 
    3, 3, 4, 3, 4, 2, 3, 4, 3, 2, 5, 2, 4, 2, 3, 4, 5, 3, 2, 
    3, 4, 3, 3, 2, 2, 4, 7, 3, 2, 3, 2, 3, 2, 2, 2, 2, 6, 4, 
    3, 2, 3, 4, 5, 3, 2, 4, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 3, 
    4, 8, 4, 4, 2, 5, 3, 3, 3, 2, 3, 2, 2, 6, 4, 4, 4, 4, 5, 
    3, 3, 4, 3, 3, 2, 2, 3, 4, 3, 5, 6, 2, 2, 2, 3, 3, 3, 2, 
    6, 3, 2, 3, 3, 2, 2, 5, 2, 2, 3, 2, 4, 3, 4, 2, 6, 2, 4, 
    3, 2, 3, 5, 2, 2, 3, 3, 4, 2, 2, 3, 2, 3, 2, 2, 5, 2, 2, 
    2, 2, 5, 2, 4, 2, 3, 2, 3, 4, 6, 3, 3, 3, 2, 3, 2, 5, 2, 
    2, 4, 3, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 6, 3, 3, 3, 3, 3, 
    2, 4, 3, 4, 3, 2, 5, 2, 3, 2, 3, 5, 2, 2, 2, 3, 2, 2, 3, 
    2, 5, 2, 4, 3, 2, 2, 3, 3, 3, 3, 4, 4, 2, 2, 3, 3, 4, 3, 
    2, 3, 5, 4, 4, 2, 3, 3, 2, 3, 5, 4, 4, 2, 2, 3, 3, 5, 3, 
    3, 6, 3, 3, 2, 8, 3, 2, 2, 3, 2, 3, 6, 2, 6, 3, 3, 4, 2, 
    3, 5, 2, 5, 2, 4, 3, 2, 3, 2, 4, 4, 3, 2, 3, 2, 4, 2, 5, 
    3, 3, 4, 3, 2, 2, 2, 3, 4, 3, 4, 2, 2, 2, 3, 3, 6, 2, 2, 
    3, 3, 3, 2, 2, 4, 2, 3, 3, 2, 2, 3, 2, 3, 4, 2, 2, 2, 3, 
    3, 5, 2, 2, 4, 3, 6, 3, 2, 4, 3, 3, 4, 4, 3, 3, 3, 3, 3, 
    4, 3, 4, 3, 3, 3, 2, 2, 3, 3, 2, 3, 2, 3, 3, 3, 3, 2, 2, 
    3, 2, 2, 3, 3, 3, 3, 2, 2, 4, 5, 3, 3, 5, 3, 3, 2, 5, 2, 
    5, 2, 2, 2, 4, 4, 3, 2, 2, 3, 3, 2, 3, 3, 5, 3, 3, 5, 3, 
    2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 4, 3, 3, 2, 3, 3, 3, 3, 
    2, 3, 5, 4, 2, 8, 2, 2, 5, 4, 3, 3, 6, 3, 2, 6, 4, 6, 3, 
    4, 2, 3, 3, 3, 7, 2, 3, 3, 3, 4, 2, 4, 3, 3, 2, 3, 3, 4, 
    2, 4, 4, 2, 4, 3, 2, 2, 3, 2, 3, 5, 3, 2, 4, 6, 2, 2, 5, 
    4, 3, 2, 3, 7, 5, 2, 3, 4, 2, 2, 3, 5, 2, 3, 2, 2, 4, 3, 
    2, 2, 2, 4, 3, 3, 3, 2, 3, 2, 4, 3, 4, 3, 2, 2, 5, 2, 2, 
    4, 3, 3, 4, 4, 2, 2, 4, 5, 4, 5, 5, 2, 3, 2, 3, 3, 6, 3, 
    5, 5, 4, 5, 2, 4, 3, 2, 5, 2, 5, 3, 2, 3, 2, 4, 5, 3, 2, 
    3, 6, 2, 5, 2, 3, 3, 3, 2, 2, 5, 3, 3, 2, 2, 3, 4, 3, 3, 
    4, 3, 2, 4, 3, 2, 5, 3, 2, 2, 4, 5, 4, 2, 3, 3, 3, 2, 3, 
    3, 6, 5, 2, 2, 7, 2, 4, 2, 4, 2, 4, 4, 2, 2, 3, 3, 5, 2, 
    4, 5, 2, 2, 4, 3, 6, 2, 3, 6, 2, 4, 6, 3, 2, 3, 2, 4, 2, 
    5, 3, 2, 3, 3, 2, 2, 2, 2, 2, 6, 2, 2, 2, 3, 3, 3, 3, 2, 
    2, 4, 3, 5, 2, 3, 4, 3, 2, 2, 2, 6, 2, 3, 3, 2, 3, 3, 3, 
    2, 2, 2, 4, 2, 3, 3, 3, 6, 3, 3, 3, 2, 4, 3, 3, 4, 2, 2, 
    2, 2, 2, 3, 3, 3, 4, 2, 4, 7, 2, 3, 2, 2, 2, 3, 3, 3, 3, 
    3, 5, 2, 2, 3, 2, 2, 3, 3, 5, 3, 3, 2, 2, 5, 2, 3, 3, 3, 
    3, 2, 3, 2, 6, 3, 4, 3, 3, 4, 4, 2, 2, 3, 3, 4, 2, 3, 3, 
    3, 2, 2, 2, 3, 3, 3, 2, 3, 4, 3, 2, 3, 5, 2, 2, 2, 5, 2, 
    2, 5)), row.names = c(NA, 3000L), class = "data.frame")

Ahorn · Accepted Answer

You could add geom_jitter to show the outliers (adapted from this post (apply jittering to outliers data in a boxplot with ggplot2):

my_xlab <- paste(levels(df$age_class),"
(N=",table(df$age_class),")",sep="")
df %>% 
  group_by(age_class) %>% 
  mutate(outlier = nr_trips > median(nr_trips) + IQR(nr_trips) * 1.5) %>% 
  ggplot(aes(x=age_class, y=nr_trips)) + 
  geom_boxplot(varwidth = TRUE, outlier.shape = NA)+
  scale_x_discrete(labels=my_xlab)+
  stat_summary(fun.data = "mean_cl_normal", 
               aes(shape="mean"), 
               size=4,
               colour = "red",
               geom="point") +
  scale_shape_manual("", values=c("mean"="x"))+
  theme_minimal() + 
  geom_jitter(data = function(x) dplyr::filter_(x, ~ outlier), width = 0.25, height = 0, alpha = .2, aes(color = "outliers")) +
  scale_color_manual(name = "", values = c("outliers" = "black"))

How can I indicate the frequency of outliers of boxplots in ggplot?

Answers (1)

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