I am trying to understand what is shown in the following boxplot given the information from the Wikipedia article on the box plot.

The problem is that we see no mean, and only whiskers in one direction.

So what are my Q1 Q2 Q3 Q4 in this case and why is not mean shown?


  • $\begingroup$ Is this the entire graph? $\endgroup$ – Kontorus Jul 14 '16 at 13:52
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    $\begingroup$ The image appears to be mangled any way. No titles, no numeric axis labels, ... But... boxplots don't usually show means any way. Minimally they show medians, quartiles, minimum and maximum. Tell us more about the data and (regrettably) the software used. If 25% or more of the data equal the minimum, the lower quartile does too. If 50% or more of the data equal the maximum, the median does too. (For data that bunched, the box plot may be a poor choice.) $\endgroup$ – Nick Cox Jul 14 '16 at 13:54
  • $\begingroup$ See stats.stackexchange.com/questions/68069/… $\endgroup$ – Nick Cox Jul 14 '16 at 13:55
  • $\begingroup$ I can't find this exact graph on the linked site. $\endgroup$ – Michael M Jul 14 '16 at 13:58
  • $\begingroup$ "If 50% or more of the data equal the maximum, the median does too." That is true, but also true of the minimum, more likely to be pertinent here. $\endgroup$ – Nick Cox Jul 14 '16 at 14:00

If this is your entire graph:

Median and Q1 are all at the bottom. Your data is not normally distributed (almost all of your data is that one value at the bottom.)

  • $\begingroup$ So q1 q2 and mean are all at the bottom and then q3 q4 are shown. That makes sense. $\endgroup$ – user3139545 Jul 14 '16 at 14:09
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    $\begingroup$ Regardless of whether the mean is shown at all, it cannot equal the minimum unless all values are identical. $\endgroup$ – Nick Cox Jul 15 '16 at 1:02
  • $\begingroup$ The median might be at the bottom, but the mean will not be. $\endgroup$ – Kontorus Jul 15 '16 at 13:41

I am guessing that what you have here would be a dynamite plot [1], rather than a boxplot; also sometimes called a detonator plot. The reason I think so is the absence of the low end of the box, which should be present if it's a boxplot with median = lower hinge = min, while the bottom of the bar is usually not drawn in a dynamite plot.

However, in any case boxplots don't normally show means. (Further, there are only three quartiles, rather than four.)

Dynamite plots do typically show means (represented by the top of the bar), though they sometimes show other things.

In the case that this is a dynamite plot, you'd read the information this way (here I annotate your plot):

annotated dynamite plot

[I don't recommend these plots, by the way; I regard them as information-poor displays, but they're widely used in some areas of science, so we need to be able to read them.]

[1]: "Dynamite plots", Vanderbilt Biostatistics Wiki Dept. of Biostatistics, Vanderbilt University http://biostat.mc.vanderbilt.edu/wiki/Main/DynamitePlots

  • 1
    $\begingroup$ Detonator plot is another name in use. $\endgroup$ – Nick Cox Jul 15 '16 at 1:00
  • $\begingroup$ @Nick Thanks; a quick google search seems to bring it up in connection with Stata in particular. $\endgroup$ – Glen_b Jul 15 '16 at 1:06
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    $\begingroup$ Indeed, a Stata user, not me, as I recall believes that he invented that term and he introduced it to the Stata community. My main criticisms of the plot are 1. So little is shown about the data. 2. Emphasis is on comparison with zero, often not a substantive question. 3. If the whisker is intended to show uncertainty it should be reflected down as well as up. 4. The graph design is not compatible with logarithmic scale, so often better. $\endgroup$ – Nick Cox Jul 15 '16 at 1:19

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