Skip to main content
25 votes
Accepted

What is 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. ...
COOLSerdash's user avatar
21 votes
Accepted

What's the history of box plots, and how did the "box and whiskers" design evolve?

Chief Executive Officer summary The history is much longer and more complicated than many people think it is. Executive summary The history of what Tukey called box plots is tangled up with that ...
Nick Cox's user avatar
  • 58.5k
20 votes

How should we do boxplots with small samples?

I believe that this is a case where software misleads users. So my answer to (1) is "no." When we try to "summarize" a sample of 2 values, or even 5, with a display containing 5 ...
Russ Lenth's user avatar
  • 20.7k
18 votes

Missing quartile in boxplot

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 ...
mkt's user avatar
  • 18.9k
18 votes
Accepted

How should we do boxplots with small samples?

What R implementations (should) do is for developers and users of that software. I wish to comment more broadly on limitations of box plots. This overlaps a little with points made in other answers, ...
Nick Cox's user avatar
  • 58.5k
17 votes

Visualize a continuous variable against a binary variable

Boxplots lose an enormous amount of information, since they condense all data into just five summary statistics (the median, the box and the whiskers) plus what is unhappily called "outliers"...
Stephan Kolassa's user avatar
16 votes

Visualize a continuous variable against a binary variable

I usually do overlayed histograms. E.g. https://stackoverflow.com/questions/49533978/multiple-histograms-in-python
Brady Gilg's user avatar
15 votes

How should we do boxplots with small samples?

This question touches on the intersection of statistics and software engineering. The statistical part of the question is uncontroversial: the boxplots, like many other statistics and data ...
Tim's user avatar
  • 140k
14 votes

Reading box-and-whisker plots: possible to glean significant differences between groups?

Yes, you can. At least in an approximate sense. I outline how below (and indeed there's a relationship to "box-overlap" as you suggest) along with some caveats and limitations. But first let'...
Glen_b's user avatar
  • 286k
13 votes

How to interpret whiskers of a box plot when there are outliers?

The question admits confusion and is itself contradictory. If whiskers extend to the extremes, then how can there be plotted data points beyond them? Let's back up. (Incidentally, the term flier is ...
Nick Cox's user avatar
  • 58.5k
13 votes
Accepted

box plot in R: Do the outliers count when the quantiles are being determined?

R -- like many, but not all programs -- mostly uses Tukey's definition* of how to draw a boxplot. The entire original sample is used to calculate the hinges (where the box-ends are drawn). Hinges ...
Glen_b's user avatar
  • 286k
12 votes
Accepted

Box plot notches vs. Tukey-Kramer interval

As far as the notched boxplot goes, the McGill et al [1] reference mentioned in your question contains pretty complete details (not everything I say here is explicitly mentioned there, but ...
Glen_b's user avatar
  • 286k
12 votes
Accepted

Understanding and Interpreting letter value boxplots

The key term is letter-value (box)plots and the key reference is now Hofmann, Heike, Wickham, Hadley and Kafadar, Karen. 2017. Letter-value plots: Boxplots for large Data. Journal of Computational and ...
Nick Cox's user avatar
  • 58.5k
11 votes
Accepted

Boxplot | 5-Number-Summary

To clarify your doubt, consider the following example using the standard definition of the boxplot. Suppose we have the following observations $x = (-40,0, 2, 3, 4,10, 40)$. The median is 3, the first ...
utobi's user avatar
  • 11.9k
10 votes
Accepted

Box Plot Upper Fence is greater than Max

Yes, it is fairly normal for the upper fence to be greater than the maximum. That's the point of the fences -- with a Normal or light-tailed distribution, there will often be no points beyond the ...
Thomas Lumley's user avatar
10 votes

Is a boxplot useful, when it doesn't even look like a box?

The boxplot doesn't visualize your data effectively. (For a discussion of the advantages and disadvantages of boxplots see How should we do boxplots with small samples? .) Other types of graphs (...
dipetkov's user avatar
  • 10.5k
10 votes
Accepted

Is a boxplot useful, when it doesn't even look like a box?

Visualisations need to be chosen based on the properties of the data and the message you are trying to convey. Clearly, boxplots do not communicate the distribution of this data well. Given that you ...
mkt's user avatar
  • 18.9k
9 votes

Why doesn't the fact that 1 median is lower than another median, mean that most in group 1 are less than most in group 2?

Here's the smallest counter-example I could find : A ([1, 4, 10]) and B ([0, 6, 9]) have the same average (...
Eric Duminil's user avatar
9 votes

Outlier detection for skewed data

For this kind of data, and any other univariate distribution, I have these recommendations. 1. Use what context you have to hand about the data. What is expected? What is or would be surprising or ...
Nick Cox's user avatar
  • 58.5k
9 votes

Missing quartile in boxplot

The "box" in a boxplot extends from the first to the third quartile, i.e., from the 25th to the 75th percentile. Visually, this means that your 25th percentile is around 6 messages, and your 75th ...
Stephan Kolassa's user avatar
9 votes

How should we do boxplots with small samples?

I consider the question "What's the smallest sample size for which a box-and-whiskers plot is a useful visual summary" to be about a rule-of-thumb for making good plots. (The question "...
dipetkov's user avatar
  • 10.5k
9 votes

Why use bar chart with error whiskers instead of box plot?

Personally, I have never encountered a good use case for bar plots and think it's mostly inertia in some fields that leads to their continued use. If you like Tufte's ideas about data-ink ratios, it'...
mkt's user avatar
  • 18.9k
9 votes
Accepted

Why use bar chart with error whiskers instead of box plot?

Realistically, the reason people do most of the things they do, is tradition / habit. 'Such-and-such is what I learned in graduate school, it's what I've always done, it's what everyone else in my ...
gung - Reinstate Monica's user avatar
8 votes

What is the basis for the Box and Whisker Plot definition of an outlier?

The word 'outlier' is often assumed to mean something like 'a data value that is erroneous, misleading, mistaken or broken and should therefore be omitted from analysis', but that is not what Tukey ...
Michael Lew's user avatar
  • 16.2k
8 votes

How should we do boxplots with small samples?

Just curious -- Looking outside of R with the same data... Stata SPSS SAS Enterprise Guide MATLAB (Statistics and Machine Learning tools) Minitab I was most curious about Minitab, but our virtual ...
Russ Lenth's user avatar
  • 20.7k
7 votes
Accepted

R: Box-plot on log scale vs. log-transforming *then* creating box-plot: Don't get same result

Obviously, the box with the median "belt" looks the same. The difference are the whiskers. In the default settings, ?boxplot tells us that If ‘range’ is positive,...
Horst Grünbusch's user avatar
7 votes

What information does a Box Plot provide that a Histogram does not?

If I show you a histogram and ask you where the median is, you might be quite some time figuring it out... and then you'll only get an approximation to it. If I do the same with a boxplot you have it ...
Glen_b's user avatar
  • 286k
7 votes

What are good data visualization techniques to compare distributions?

There is a concept specifically for comparing distributions, which ought to be better known: the relative distribution. Let's say we have random variables $Y_0, Y$ with cumulative distribution ...
7 votes

Violin plot or bean plot? What are the advantages of each?

I don't know about bean plots but for small sample sizes violin plots may be unstable and I would prefer to just show the raw data with a rug plot or spike histogram. Sometimes I superimpose a violin ...
Frank Harrell's user avatar
7 votes
Accepted

How are whiskers in a Boxplot of different lengths?

Not necessarily. The whiskers actually end at the highest point within $Q3+1.5R$ and at the lowest point above $Q1-1.5R$. So for instance if $Q3+1.5R=100$ and the highest value in your sample is $90$ ...
Satwik Bhattamishra's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible