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

Histograms give a good sense of the distribution of a variable. Box plots attempt to do the same thing however, don't give as good of a picture of the distribution of this variable.

I don't understand why people use box plots. Histograms are better in every way. Is there a reason I would use both of them?

The only thing I think that box plots provide is: outliers! It tells us which observations may be outliers.

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Is Histogram worse in every way than a representation of the whole distribution ? – Aerandal Mar 20 at 14:16
Depends on what you want, with a box plot you can have some precise values (eg median, P75), that you do not have with an histogram. It displays less information, but is more synthetic. My point is that even an histogram is a simplification and a waste of information compared to the whole distribution. But it can be easier to use – Aerandal Mar 20 at 14:24
A contrary viewpoint about the utility of histograms has been cogently expressed, and well illustrated, in the highly upvoted post at stats.stackexchange.com/a/51753 (which can be found by searching our site for "histogram"). – whuber Mar 20 at 14:35
Interesting thought--but increasing the bin size would reduce the histogram to a boxplot-like figure while retaining its unfortunate dependence on the choice of cutpoints. IMHO, the real merits of boxplots can best be appreciated by studying Tukey's use of the N-letter summary for exploratory analysis of multivariate data and remembering that he was calculating with pencil and paper at the time. For visualizations like a "wandering schematic trace" other univariate summaries of conditional responses, like histograms or violin plots, simply would not work. – whuber Mar 20 at 15:24
The two failures (imo) of the histogram happen when there are few samples or when the boxes are the wrong sizes. The weakness of a good boxplot (and I'm thinking JMP variability when I say it) are multi-modality, and fine detail. One place where the boxplot shines is when there are few samples. I also like it when there are a number of interacting variables at different levels - thus the JMP variability plot. – EngrStudent Mar 21 at 0:20

The fact that box plots provide more of a summary of a distribution can also be seen as an advantage in certain cases. Sometimes when we're comparing distributions we don't care about overall shape, but rather where the distributions lie with regard to one another. Plotting the quantiles side by side can be a useful way of doing this without distracting us with other details that we may not care about.

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This is the best answer. Boxplots are better for comparing distributions than histograms! – kjetil b halvorsen Mar 20 at 19:48

In the univariate case, box-plots do provide some information that the histogram does not (at least, not explicitly). That is, it typically provides the median, 25th and 75th percentile, min/max that is not an outlier and explicitly separates the points that are considered outliers. This can all be "eyeballed" from the histogram (and may be better to be eyeballed in the case of outliers).

However, the much bigger advantage is in comparing distributions across many different groups all at once. With 10+ groups, this is a tiring task with side-by-side histograms, but very easy with box plots.

As you mentioned, violin plots (or bean plots) are somewhat more informative alternatives. However, they require slightly more statistical knowledge than the box plots (i.e. if presenting to a non-statistical audience, it may be a little more intimidating) and box-plots have been around much longer than kernel density estimators, hence their greater popularity.

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+1. Correction though, box-plots provide medians, not means. – Greenparker Mar 21 at 0:09
Everyone can be right. Box plots as usually plotted show medians (I've seen this denied, but do not recall seeing an example). But some implementations allow you to show means as well. That's often a good idea. – Nick Cox Mar 21 at 0:46
Thanks for pointing that out. I keep (incorrectly) thinking it's usually the mean, which could lead to some very weird plots in extreme cases. – Cliff AB Mar 21 at 4:18

The fundamental issue is that histograms heavily rely on the bin size. It is difficult to determine this a priori.

However, kernel density plots are another alternative we could use instead. We should also consider using violin plots, as they are ultimately best of both worlds.

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This does not really address the question. – Greenparker Mar 23 at 16:13