How to draw a box plot in Matplotlib without a dataset?

Matplotlib's bxp function could be used. To show the information that is important in your case, instead of drawing the box between the 25^th and the 75^th percentile, it could be drawn between the 10^th and 90^th. Optionally labels, a legend or an accompanying text could explain the meaning of the elements of the boxplot.

import matplotlib.pyplot as plt

median = 5
average = 6
min_val = 1
max_val = 9
p10 = 3
p90 = 8
stats = [{'mean': average, 'med': median, 'q1': p10, 'q3': p90, 'whislo': min_val, 'whishi': max_val}]

fig, ax = plt.subplots()
ax.bxp(stats, showfliers=False, showmeans=True)

names = {'mean': 'average', 'med': 'median', 'q1': 'perc 10', 'q3': 'perc 90', 'whislo': 'min val', 'whishi': 'max val'}
for s in stats[0]:
    ax.text(1.1, stats[0][s], names[s], va='center', ha='left')
plt.xticks([1], ['boxplot 1'])
plt.show()

The following code adds two extra entries to stats dictionary for the average plus and minus the standard deviation. These extra entries are ignored by ax.bxp and can be plotted in a separate step. As an example, they are plotted with a circular marker.

Note that the plot gets quite full. Also, it might be confusing to add mean and sdev while the five other elements are percentile-based. It can be especially confusing when the sdev would fall outside the rectangular box.

The example shows how 3 different boxplots could look like:

import matplotlib.pyplot as plt
import numpy as np

def get_stats(x):
    return {'mean': x.mean(), 'med': np.median(x), 'q1': np.percentile(x, 10), 'q3': np.percentile(x, 90),
            'whislo': x.min(), 'whishi': min(10, x.max()),
            'minus sdev': x.mean() - x2.std(), 'plus sdev': x.mean() + x.std()}

median = 5
average = 6
min_val = 1
max_val = 9
p10 = 3
p90 = 8
sdev = 1.5
stats1 = {'mean': average, 'med': median, 'q1': p10, 'q3': p90, 'whislo': min_val, 'whishi': max_val,
          'minus sdev': average - sdev, 'plus sdev': average + sdev}

x2 = np.random.zipf(2.6, 100)
stats2 = get_stats(x2)

x3 = np.random.normal(np.tile(np.random.uniform(2, 8, 5), 100), 1)
stats3 = get_stats(x3)

stats = [stats1, stats2, stats3]
names = {'mean': 'average', 'med': 'median', 'q1': 'perc 10', 'q3': 'perc 90', 'whislo': 'min val', 'whishi': 'max val',
         'minus sdev': 'minus sdev', 'plus sdev': 'plus sdev'}

fig, ax = plt.subplots()
ax.bxp(stats, showfliers=False, showmeans=True)
for i in range(1, len(stats) + 1):
    ax.scatter([i, i], [stats[i - 1]['minus sdev'], stats[i - 1]['plus sdev']], marker='o', color='g')
    if i == 1:  # add explanory texts
        for s in stats[i - 1]:
            ax.text(i + .2, stats[i - 1][s], names[s], va='center', ha='left')

ax.set_xticks(range(1, len(stats) + 1))
ax.set_xticklabels(['imaginary example', 'zipf(2.6)', 'combined gaussians'])
plt.show()