如何在 ggplot 中的箱线图上指示异常值的频率？
How can I indicate the frequency of outliers of boxplots in ggplot?
我有以下箱线图：
它们是使用以下代码生成的：
my_xlab <- paste(levels(adpt_info$age_class),"\n(N=",table(adpt_info$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()
如您所见，箱线图有一个 alpha 值，该值应该表示出现了多少具有相同值的异常值。 nr_trips 是整数值。
我想做的是将 alpha 值的图例添加到绘图中，或者以不同的方式指示出现的情况。像这样，在我看来，它不能很好地显示分布的差异。
感谢您的帮助！
数据摘录：
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")
您可以添加 geom_jitter 以显示异常值（改编自此 post (apply jittering to outliers data in a boxplot with ggplot2):
my_xlab <- paste(levels(df$age_class),"\n(N=",table(df$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"))
我有以下箱线图：
它们是使用以下代码生成的：
my_xlab <- paste(levels(adpt_info$age_class),"\n(N=",table(adpt_info$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()
如您所见，箱线图有一个 alpha 值，该值应该表示出现了多少具有相同值的异常值。 nr_trips 是整数值。
我想做的是将 alpha 值的图例添加到绘图中，或者以不同的方式指示出现的情况。像这样，在我看来，它不能很好地显示分布的差异。
感谢您的帮助！
数据摘录：
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")
您可以添加 geom_jitter 以显示异常值（改编自此 post (apply jittering to outliers data in a boxplot with ggplot2):
my_xlab <- paste(levels(df$age_class),"\n(N=",table(df$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"))