4
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Is there a recommended way to illustrate a heavily skewed distribution using a boxplot? For example, my boxplot looks like so:

enter image description here

It's very difficult to know what the median value is for the green boxplot. If I specify the range using ylim(0, 1), as far as I can tell ggplot2 removes points outside of the range in the boxplot calculation. I'm creating my plot using the following R code:

ggplot(df, aes(x=x, y=y)) + geom_boxplot(aes(colour=status)) 

I am aware that I can plot this using a histogram, but it's difficult to visuallly compare the two groups using a histogram.

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  • 1
    $\begingroup$ What about a qqplot or a relative distribution plot? When the goal is to compare the distributions, it might be better with a plot specially made for distribution comparison, than with two parallell plots. $\endgroup$ – kjetil b halvorsen Dec 12 '16 at 10:54
  • 2
    $\begingroup$ Zero-skewed is not a good term for "skewed because there are lots of zeros" as zero skewness otherwise means skewness of zero. But it's not difficult to determine the median on the right at all: it's zero, as clearly at least 75% of values are zero. I'd use a quantile plot for these data. Can you post them? $\endgroup$ – Nick Cox Dec 12 '16 at 10:56
  • $\begingroup$ @kjetilbhalvorsen - good idea, I have used geom_freqpoly() previously. @nickcox thanks for explaining - did not realize I was using incorrect term. I'll prepare a sample of data to post $\endgroup$ – celenius Dec 12 '16 at 11:01
  • 1
    $\begingroup$ See stats.stackexchange.com/questions/140090/… for a quantile-box plot for a dataset with several zeros. But your data appear more skewed yet. $\endgroup$ – Nick Cox Dec 12 '16 at 11:02
  • 1
    $\begingroup$ Independently of other suggestions, using a transformed scale might also help, say cube root or square root. $\endgroup$ – Nick Cox Dec 12 '16 at 12:14
1
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You can use violine 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, 
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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: Violin plot

$\endgroup$

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