Given quartiles, how do I draw a box-whisker using MATLAB, matplotlib, gnuplot, or some other package?

Question

I'm given a number of data points like this:

2.50%   3.45
25.00%  4.19
50.00%  4.7
75.00%  5.42
97.50%  6.87

This defines a complete box-whisker element for a plot. I'm not sure how I can plot this. All the methods I've looked up so far (MATLAB, matplotlib, gnuplot) construct boxes from the original data. I don't have access to the original data, but I do have all the information I should need to draw the boxes.

What's the best way to draw the boxes/whiskers without the data?

Answer 1

You can use the following trick in Matlab:

Let x be a vector containing your percentile values:

x = [3.45 4.19 4.7 5.42 6.87];

Let's extend this vector by repeating the median, appending it to the end:

y = [x x((1+end)/2)];

Now the 75, 50 and 25 percentiles of y, considered as a data vector, coincide with the desired values:

>>prctile(y,75)
ans =
    5.4200
>>prctile(y,50)
ans =
    4.7000
>>prctile(y,25)
ans =
    4.1900

So: simply call boxplot using this extended vector as data:

boxplot([x x((1+end)/2)])

A nice thing of this approach is that you can use all the fancy options of boxplot to customize the plot.

The trick can probably be applied to matplotlib and gnuplot as well.