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Another example: using a colorbar to show bar height

import matplotlib.pyplot as plt
from matplotlib.cm import ScalarMappable

data_x = [0,1,2,3]
data_hight = [60,60,80,100]

data_hight_normalized = [x / max(data_hight) for x in data_hight]

fig, ax = plt.subplots(figsize=(15, 4))

my_cmap = plt.cm.get_cmap('GnBu')
colors = my_cmap(data_hight_normalized)

rects = ax.bar(data_x, data_hight, color=colors)

sm = ScalarMappable(cmap=my_cmap, norm=plt.Normalize(0,max(data_hight)))

sm.set_array([])

cbar = plt.colorbar(sm)
cbar.set_label('Color', rotation=270,labelpad=25)

plt.xticks(data_x)    
plt.ylabel("Y")

plt.title('How to plot a bar chart with a colorbar with matplotlib ?')

plt.savefig("bar_chart_with_colorbar_03.png", bbox_inches='tight')

plt.show()

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Another example: using a colorbar to show bar height

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