Drawing a boxplot of the bins of histograms for histogram comparation

Question

I'm trying to compare five histograms (maybe in an unorthodox, non-traditional way). I already plotted the histograms and overlapped their bins in a graph. Now I want to plot boxplots of the distribution of the data in every interval (each interval have counts of the 5 histograms, so I'm asking for a kind of nested distribution). Graphically, this should look like the attached picture.

This is my code for the creation of the overlapped histograms.

import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt

u30_diameter_01 = pd.Series([6.76, 5.03, 6.57, 5.52, 8.81, 9.50, 4.96, 6.19, 5.61, 4.86, 4.41, 6.04, 6.39, 4.61, 6.90, 6.38, 6.20, 6.75, 4.76, 6.18, 6.13, 7.95, 4.22, 6.16, 8.40, 6.90, 6.77, 6.11, 6.15, 6.43])
u30_diameter_02 = pd.Series([4.98, 5.16, 6.43, 3.93, 5.41, 6.39, 6.35, 5.43, 6.69, 7.10, 7.55, 5.92, 6.50, 5.36, 7.27, 4.10, 6.89, 4.82, 4.34, 5.67, 8.95, 7.53, 4.91, 5.30, 6.62, 6.90, 5.98, 6.05, 4.37, 6.42, 5.03, 7.78, 6.28, 7.81, 5.81, 5.99, 6.22, 6.48, 4.43, 5.18])
u30_diameter_03 = pd.Series([5.80, 5.72, 6.19, 5.69, 4.19, 4.82, 6.32, 6.14, 6.59, 4.90, 6.39, 5.93, 5.17, 6.00, 6.64, 7.48, 5.61, 5.79, 4.79, 5.99, 5.11, 6.08, 6.68, 5.84, 6.88, 6.81, 6.07, 4.55, 6.20, 5.50])
u30_diameter_04 = pd.Series([5.21, 7.85, 6.48, 4.44, 6.91, 6.30, 8.51, 5.99, 7.74, 5.47, 6.19, 8.44, 8.03, 8.37, 6.80, 6.49, 5.65, 6.06, 7.04, 4.55, 6.76, 7.99, 5.64, 5.97, 6.21])
u30_diameter_05 = pd.Series([7.24, 7.42, 6.85, 8.14, 7.03, 6.52, 5.82, 6.92, 7.44, 7.91, 7.18, 7.99, 6.19, 7.44, 7.37, 6.54, 7.11, 7.77, 8.67, 8.35, 7.12, 5.10, 8.29, 6.36, 7.81])
u30_diameter = pd.concat([u30_diameter_01, u30_diameter_02, u30_diameter_03, u30_diameter_04, u30_diameter_05], ignore_index=True).to_frame()

u30_diameter.columns = ['Value']
u30_diameter['Photo'] = pd.Series(['1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1','1',
'2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2','2',
'3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3','3',
'4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4','4',
'5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5','5'])
diameter_range = np.arange(3.75,9.75,0.5)

sns.histplot(data=u30_diameter, x="Value", hue="Photo", element="step", bins=12)

This is a extra code for the creation of the boxes (I manually count for how the counts in every interval).

import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt

u30_d_01 = pd.Series([1,4,1,0,0])
u30_d_02 = pd.Series([3,2,3,2,0])
u30_d_03 = pd.Series([3,6,3,1,1])
u30_d_04 = pd.Series([2,4,4,3,0])
u30_d_05 = pd.Series([8,6,11,5,2])
u30_d_06 = pd.Series([4,9,5,3,3])
u30_d_07 = pd.Series([5,3,2,4,5])
u30_d_08 = pd.Series([0,3,1,0,1])
u30_d_09 = pd.Series([1,2,0,4,4])
u30_d_10 = pd.Series([1,0,0,3,3])
u30_d_11 = pd.Series([1,1,0,0,1])
u30_d_12 = pd.Series([1,0,0,0,0])

u30_d = pd.concat([u30_d_01, u30_d_02, u30_d_03, u30_d_04, u30_d_05, u30_d_06, u30_d_07, u30_d_08, u30_d_09, u30_d_10, u30_d_11, u30_d_12], ignore_index=True).to_frame()
u30_d.columns = ['Value']

u30_d['Photo'] = pd.Series([
'1','1','1','1','1','2','2','2','2','2','3','3','3','3','3','4','4','4','4','4',
'5','5','5','5','5','6','6','6','6','6','7','7','7','7','7','8','8','8','8','8',
'9','9','9','9','9','10','10','10','10','10','11','11','11','11','11','12','12','12','12','12'
])

fig, ax = plt.subplots(figsize=(5,5))
sns.boxplot(ax=ax,x='Photo',y='Value',data=u30_d)
ax.set_xlabel('Diameter, \u03BCm')
ax.set_ylabel('Count')
fig.savefig('U30_d_box.png', facecolor='white', edgecolor='none')

This is a picture, that roughly represents what I'm aiming.

Thank you!

Answer 1

On your histogram x axis represents the value, while y axis the count. For this reason a boxplot (which represent the quantile distribution of a quantity) cannot be vertical but horizontal since it has to represent the quantile distribution across 'Value' axis.
That being said, you may do that with a subplot:

fig, ax = plt.subplots(2, 1, sharex = 'all', figsize = (6, 8))

sns.histplot(ax = ax[0], data=u30_diameter, x="Value", hue="Photo", element="step", bins=12)
sns.boxplot(ax = ax[1], data = u30_diameter, x = 'Value', y = 'Photo', hue = 'Photo', dodge = False)

plt.show()

---

If you want to plot boxplot of count for each bin, then you have to compute bins and counts:

n_bins = 12

fig, ax = plt.subplots()

_, bins, _ = ax.hist(u30_diameter['Value'], bins = n_bins)
counts = []

for photo in u30_diameter['Photo'].unique():
    n, _, _ = ax.hist(u30_diameter[u30_diameter['Photo'] == photo]['Value'], bins = bins)
    counts.append(n)
counts = np.array(counts)

bins = [(bins[i + 1] + bins[i])/2 for i in range(n_bins)]

Now you can erase previous plot you used to compute bins and counts and draw the plots you want:

ax.cla()

sns.histplot(ax=ax, data=u30_diameter, x="Value", hue="Photo", element="step", bins=12)
ax.boxplot(counts, positions=bins, manage_ticks=False, patch_artist=True, boxprops={'facecolor': 'blue', 'alpha': 0.5})

plt.show()