DOC: Rewrite the example illustrating bxp()

Previously, the example essentially replicated illustrations of a lot
of styling variants, which have already been shown for `boxplot()`.
Compare:
- https://matplotlib.org/3.8.3/gallery/statistics/bxp.html
- https://matplotlib.org/3.8.3/gallery/statistics/boxplot.html

I believe it's not necessary to iterate through all that again. Instead,
this rewrite focuses on the relation between `boxplot_stats()`, `bxp()`
and `boxplot`. And it shows how to use `bxp()` in isolation.

galleries/examples/statistics/bxp.py

@@ -1,107 +1,65 @@
 """
-=======================
-Boxplot drawer function
-=======================
-
-This example demonstrates how to pass pre-computed box plot
-statistics to the box plot drawer. The first figure demonstrates
-how to remove and add individual components (note that the
-mean is the only value not shown by default). The second
-figure demonstrates how the styles of the artists can
-be customized.
-
-A good general reference on boxplots and their history can be found
-here: http://vita.had.co.nz/papers/boxplots.pdf
-"""
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-import matplotlib.cbook as cbook
+=============================================
+Separate calculation and plotting of boxplots
+=============================================
 
-# fake data
-np.random.seed(19680801)
-data = np.random.lognormal(size=(37, 4), mean=1.5, sigma=1.75)
-labels = list('ABCD')
-
-# compute the boxplot stats
-stats = cbook.boxplot_stats(data, labels=labels, bootstrap=10000)
+Drawing a `~.axes.Axes.boxplot` for a given data set, consists of two main operations,
+that can also be used separately:
 
-# %%
-# After we've computed the stats, we can go through and change anything.
-# Just to prove it, I'll set the median of each set to the median of all
-# the data, and double the means
+1. Calculating the boxplot statistics: `matplotlib.cbook.boxplot_stats`
+2. Drawing the boxplot: `matplotlib.axes.Axes.bxp`
 
-for n in range(len(stats)):
-    stats[n]['med'] = np.median(data)
-    stats[n]['mean'] *= 2
+Thus, ``ax.boxplot(data)`` is equivalent to ::
 
-print(list(stats[0]))
+    stats = cbook.boxplot_stats(data)
+    ax.bxp(stats)
 
-fs = 10  # fontsize
-
-# %%
-# Demonstrate how to toggle the display of different elements:
+All styling keyword arguments are identical between `~.axes.Axes.boxplot` and
+`~.axes.Axes.bxp`, and they are passed through from `~.axes.Axes.boxplot` to
+`~.axes.Axes.bxp`. However, the *tick_labels* parameter of `~.axes.Axes.boxplot`
+translates to a generic *labels* parameter in `.boxplot_stats`, because the labels are
+data-related and attached to the returned per-dataset dictionaries.
 
-fig, axs = plt.subplots(nrows=2, ncols=3, figsize=(6, 6), sharey=True)
-axs[0, 0].bxp(stats)
-axs[0, 0].set_title('Default', fontsize=fs)
+The following code demonstrates the equivalence between the two methods.
 
-axs[0, 1].bxp(stats, showmeans=True)
-axs[0, 1].set_title('showmeans=True', fontsize=fs)
+"""
+# sphinx_gallery_thumbnail_number = 2
 
-axs[0, 2].bxp(stats, showmeans=True, meanline=True)
-axs[0, 2].set_title('showmeans=True,\nmeanline=True', fontsize=fs)
+import matplotlib.pyplot as plt
+import numpy as np
 
-axs[1, 0].bxp(stats, showbox=False, showcaps=False)
-tufte_title = 'Tufte Style\n(showbox=False,\nshowcaps=False)'
-axs[1, 0].set_title(tufte_title, fontsize=fs)
+from matplotlib import cbook
 
-axs[1, 1].bxp(stats, shownotches=True)
-axs[1, 1].set_title('notch=True', fontsize=fs)
+np.random.seed(19680801)
+data = np.random.randn(20, 3)
 
-axs[1, 2].bxp(stats, showfliers=False)
-axs[1, 2].set_title('showfliers=False', fontsize=fs)
+fig, (ax1, ax2) = plt.subplots(1, 2)
 
-for ax in axs.flat:
-    ax.set_yscale('log')
-    ax.set_yticklabels([])
+# single boxplot call
+ax1.boxplot(data, tick_labels=['A', 'B', 'C'],
+            patch_artist=True, boxprops={'facecolor': 'bisque'})
 
-fig.subplots_adjust(hspace=0.4)
-plt.show()
+# separate calculation of statistics and plotting
+stats = cbook.boxplot_stats(data, labels=['A', 'B', 'C'])
+ax2.bxp(stats, patch_artist=True, boxprops={'facecolor': 'bisque'})
 
 # %%
-# Demonstrate how to customize the display different elements:
-
-boxprops = dict(linestyle='--', linewidth=3, color='darkgoldenrod')
-flierprops = dict(marker='o', markerfacecolor='green', markersize=12,
-                  linestyle='none')
-medianprops = dict(linestyle='-.', linewidth=2.5, color='firebrick')
-meanpointprops = dict(marker='D', markeredgecolor='black',
-                      markerfacecolor='firebrick')
-meanlineprops = dict(linestyle='--', linewidth=2.5, color='purple')
-
-fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(6, 6), sharey=True)
-axs[0, 0].bxp(stats, boxprops=boxprops)
-axs[0, 0].set_title('Custom boxprops', fontsize=fs)
-
-axs[0, 1].bxp(stats, flierprops=flierprops, medianprops=medianprops)
-axs[0, 1].set_title('Custom medianprops\nand flierprops', fontsize=fs)
+# Using the separate functions allows to pre-calculate statistics, in case you need
+# them explicitly for other purposes, or to reuse the statistics for multiple plots.
+#
+# Conversely, you can also use the `~.axes.Axes.bxp` function directly, if you already
+# have the statistical parameters:
 
-axs[1, 0].bxp(stats, meanprops=meanpointprops, meanline=False,
-              showmeans=True)
-axs[1, 0].set_title('Custom mean\nas point', fontsize=fs)
+fig, ax = plt.subplots()
 
-axs[1, 1].bxp(stats, meanprops=meanlineprops, meanline=True,
-              showmeans=True)
-axs[1, 1].set_title('Custom mean\nas line', fontsize=fs)
+stats = [
+    dict(med=0, q1=-1, q3=1, whislo=-2, whishi=2, fliers=[-4, -3, 3, 4], label='A'),
+    dict(med=0, q1=-2, q3=2, whislo=-3, whishi=3, fliers=[], label='B'),
+    dict(med=0, q1=-3, q3=3, whislo=-4, whishi=4, fliers=[], label='C'),
+]
 
-for ax in axs.flat:
-    ax.set_yscale('log')
-    ax.set_yticklabels([])
+ax.bxp(stats, patch_artist=True, boxprops={'facecolor': 'bisque'})
 
-fig.suptitle("I never said they'd be pretty")
-fig.subplots_adjust(hspace=0.4)
 plt.show()
 
 # %%
@@ -112,4 +70,5 @@
 #    in this example:
 #
 #    - `matplotlib.axes.Axes.bxp`
+#    - `matplotlib.axes.Axes.boxplot`
 #    - `matplotlib.cbook.boxplot_stats`