Solved – Boxplot interpretation

boxplot

I'm taking an introductory online statistics class. Unfortunately not everything is clear to me from this class. One of the chapters in the book contains an example of a Box-and-Whisker interpretation, which I can't understand. Here is the example:

The filled dots on the image indicate minimum and maximum values; an empty dot indicates an outlier.

Here is the statement that I cannot understand:

The box plot extends nearly to the lower extreme, indicating that the data is less than the median is likely at least relatively consistent, since there is not large jump between lower 25% and the minimum.

I can't understand the reasoning. How a not a large jump between the lower 25% and the minimum leads to the data being consistent for the data that is less than the median? Also what does consistent imply/mean? Does it mean that data is distributed in a certain fashion?

Best Answer

The dots you observe to the right and left of the box plot (which are joined by a red line to the plot) are probably observations falling outside the range of the box-plot.

Normal box plot contains the observations from the 25th percentile to 75th percentile which is also called the interquartile range. The red line inside the box is the 50th percentile.

Coming to the statement you have a doubt about, all it means is that the black dot is close to the left end of the box plot (which is the 25th percentile).

edit:

By consistency he seems to be hinting about the fact that the lower extreme is not far away from the 25th percentile. You cannot really comment on distribution of data using this except for the fact that there is a concentration of observations below the 25th percentile

Related Solutions

Solved – What are some alternatives to a boxplot

A boxplot isn't that complicated. After all, you just need to compute the three quartiles, and the min and max which define the range; a subtlety arises when we want to draw the whiskers and various methods have been proposed. For instance, in a Tukey boxplot values outside 1.5 times the inter-quartile from the first or third quartile would be considered as outliers and displayed as simple points. See also Methods for Presenting Statistical Information: The Box Plot for a good overview, by Kristin Potter. The R software implements a slightly different rule but the source code is available if you want to study it (see the boxplot() and boxplot.stats() functions). However, it is not very useful when the interest is in identifying outliers from a very skewed distribution (but see, An adjusted boxplot for skewed distributions, by Hubert and Vandervieren, CSDA 2008 52(12)).

As far as online visualization is concerned, I would suggest taking a look at Protovis which is a plugin-free js toolbox for interactive web displays. The examples page has very illustrations of what can be achieved with it, in very few lines.

Solved – Outliers for boxplot

I'll use R in proposing a solution. Let's simulate some data:

set.seed(1)
foo <- c(rnorm(100,0,1),5,5,5,7,7)

I see two possibilities. The first one would be to plot the boxplot and add sunflowerplots of the outliers:

bar <- boxplot(foo)
sunflowerplot(x=rep(1,length(bar$out)),bar$out,seg.col=1,add=TRUE)

sunflowerplotted outliers

The second possibility is to plot the boxplot (which creates a single point for each outlier) and add additional points for additional outliers - which are jittered horizontally (edited as per @chl's excellent suggestion):

bar <- boxplot(foo,plot=FALSE)
boxplot(foo,outline=FALSE,ylim=c(min(c(bar$stats,bar$out)),max(c(bar$stats,bar$out))))
points(jitter(rep(1, length(bar$out))), bar$out)

jittered outliers

Note that the first solution requires that your data are integers (otherwise you will run afoul of floating-point arithmetic, see question 7.31 in the R FAQ - in this case you will need to do some additional work to ensure R knows which floating point numbers should be treated as "equal").

Best Answer

Related Solutions

Solved – What are some alternatives to a boxplot

Solved – Outliers for boxplot

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