Create Boxplot from median, std, 25% and 75% values

Question

median = 3637
std = 1274.997414
perc_25 = 2627.0
perc_75 = 4238.0

I have 4 values derived from data. How can I make a Boxplot out of this? I expect a line symbolizing median, a box delimited by 25-percentile and 75-percentile and one point on each side for median+std and median-std.

Usually I need a list of values or a dataframe, but I already computed the statistics, now I just want to display them.

Answer 1

Internally, boxplot computes bxpstats with matplotlib.cbook.boxplot_stats (source), then it passes the result to Axes.bxp (source).

        bxpstats = cbook.boxplot_stats(x, whis=whis, bootstrap=bootstrap,
                                       labels=labels, autorange=autorange)

...

        artists = self.bxp(bxpstats, positions=positions, widths=widths,
                           vert=vert, patch_artist=patch_artist,
                           shownotches=notch, showmeans=showmeans,
                           showcaps=showcaps, showbox=showbox,
                           boxprops=boxprops, flierprops=flierprops,
                           medianprops=medianprops, meanprops=meanprops,
                           meanline=meanline, showfliers=showfliers,
                           capprops=capprops, whiskerprops=whiskerprops,
                           manage_ticks=manage_ticks, zorder=zorder,
                           capwidths=capwidths)

You can shortcut the first steps by designing a dictionary in the correct format:

import matplotlib.pyplot as plt

median = 3637
std = 1274.997414
perc_25 = 2627.0
perc_75 = 4238.0

bxpstats = [{'whishi': median+std,
             'whislo': median-std,
             'fliers': [],
             'q1': perc_25,
             'med': median,
             'q3': perc_75}]

ax = plt.subplot()
ax.bxp(bxpstats)

Output:

If you want several boxes add more dictionaries in the list:

bxpstats = [{'whishi': 5, 'whislo': 1, 'fliers': [6], 'q1': 2, 'med': 3, 'q3': 4},
            {'whishi': 5.5, 'whislo': 3, 'fliers': [2, 2.5, 5.7], 'q1': 4, 'med': 4.5, 'q3': 5}
           ]
ax = plt.subplot()
ax.bxp(bxpstats)

To give you the full list of parameters:

import matplotlib
matplotlib.cbook.boxplot_stats([1, 2, 3, 100])

[{'mean': 26.5,                 # mean (shown if showmeans=True)
  'iqr': 25.5,                  # q3-q1
  'cilo': -17.517500000000002,  # lower confidence interval (shown if shownotches=True)
  'cihi': 22.517500000000002,   # upper confidence interval (shown if shownotches=True)
  'whishi': 27.25,              # upper whisker
  'whislo': 1,                  # lower whisker
  'fliers': array([100]),       # outliers
  'q1': 1.75,                   # q1 (bottom of box)
  'med': 2.5,                   # median (orange line)
  'q3': 27.25}]                 # q3 (top of box)