Visualization with matplotlib — Python

In this lesson you will learn

Build a chart the object-oriented way with fig, ax = plt.subplots() and add a title, axis labels and a legend
Choose the chart type that fits the question: line, bar, scatter or histogram
Justify the number of histogram bins with the Sturges and Freedman–Diaconis rules
Recognise misleading charts and draw honest, readable ones

In 1973 the statistician Francis Anscombe published four small datasets whose means, variances, correlation coefficient and regression line are almost identical. Yet on a chart one is scattered around a straight line, one follows a curve, in the third a single outlier changes everything, and in the fourth all points but one lie on a vertical line. The lesson: before trusting the numbers, look at the data. In Python the main tool for this is matplotlib.

Figure and Axes: how a chart is built

Definition

Figure and Axes

The Figure is the whole image, the “canvas”. An Axes is one plotting area inside it: the axes, lines, title and legend. A Figure can contain several Axes. Most methods belong to the Axes: ax.plot, ax.set_title, ax.legend.

matplotlib has two styles: the short “pyplot” style such as plt.plot(...) and the object-oriented style. Always start with the second: fig, ax = plt.subplots() — such code stays clear even with several charts. In the browser the image appears under the code automatically; on your computer plt.show() opens a window and fig.savefig('chart.png', dpi=200) saves a file.

Python· Edit the code and run it again

import matplotlib.pyplot as plt

months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun']
baku = [279, 153, 426, 390, 455, 510]
ganja = [150, 306, 168, 210, 240, 265]

fig, ax = plt.subplots(figsize=(7, 4))
ax.plot(months, baku, marker='o', label='Baku')
ax.plot(months, ganja, marker='s', linestyle='--', label='Ganja')
ax.set_title('Monthly revenue by branch, 2026')
ax.set_xlabel('Month')
ax.set_ylabel('Revenue, AZN')
ax.grid(alpha=0.3)
ax.legend()
plt.show()

A line chart shows change over time. Markers show the measurement points, and different line styles separate the series even for people who cannot tell the colours apart.

Title — what the chart shows, where and when.
Axis labels with units: “Revenue, AZN”, “Height, cm”.
Legend — whenever there is more than one series.
A faint grid (grid(alpha=0.3)) — makes values easier to read without distracting.

Choosing the chart type

Question	Chart	matplotlib
How does it change over time?	line chart	`ax.plot`
How do categories compare?	bar chart	`ax.bar`, `ax.barh`
Are two numeric variables related?	scatter plot	`ax.scatter`
How are the values distributed?	histogram, box plot	`ax.hist`, `ax.boxplot`

Python· Edit the code and run it again

import numpy as np
import matplotlib.pyplot as plt

products = np.array(['Coffee', 'Cake', 'Tea', 'Juice', 'Sandwich'])
revenue = np.array([564, 540, 378, 212, 305])
order = np.argsort(revenue)

fig, ax = plt.subplots(figsize=(6, 3.5))
bars = ax.barh(products[order], revenue[order], color='#4C72B0')
ax.bar_label(bars, fmt='%d AZN', padding=3)
ax.set_xlim(0, 680)
ax.set_xlabel('Revenue, AZN')
ax.set_title('Revenue by product, Q1 2026')
print(products[order][-1], revenue.max())
plt.show()

▸ Expected output

Coffee 564

A scatter plot shows the relationship between two numeric variables. Colour can carry a third variable (c=, cmap=), and np.polyfit(x, y, 1) finds the trend line by least squares. The data below is invented: the area, number of rooms and price of flats.

Python· Edit the code and run it again

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(3)
area = rng.uniform(40, 140, 60)
rooms = np.clip(area // 30, 1, 4).astype(int)
price = 1.5 * area + 10 * rooms + rng.normal(0, 15, 60)
slope, intercept = np.polyfit(area, price, 1)
print(f'slope: {slope:.2f} thousand AZN per m2')
print(f'correlation r = {np.corrcoef(area, price)[0, 1]:.3f}')

fig, ax = plt.subplots(figsize=(6, 4))
points = ax.scatter(area, price, c=rooms, cmap='viridis', alpha=0.8)
xs = np.array([40, 140])
ax.plot(xs, slope * xs + intercept, color='red', label='trend line')
fig.colorbar(points, ax=ax, label='rooms')
ax.set_xlabel('Area, m²')
ax.set_ylabel('Price, thousand AZN')
ax.legend()
plt.show()

▸ Expected output

slope: 2.00 thousand AZN per m2
correlation r = 0.960

The viridis colour map stays readable in black-and-white print and for people with colour-vision deficiency. The correlation coefficient r is explained in detail in the next lesson.

Histograms and the number of bins

A histogram divides the value axis into equal intervals (bins) and counts the observations that fall into each one. With too few bins the shape of the distribution is lost; with too many the chart turns into a noisy “comb”. Two well-known rules give a starting point:

k = ⌈log₂ n⌉ + 1 h = 2 · IQR · n^(−1/3)

where:

knumber of bins (Sturges' rule)
hbin width (Freedman–Diaconis rule), in the data's units
nnumber of observations
IQRinterquartile range Q3 − Q1

Sturges suits roughly normal, not too large datasets; Freedman–Diaconis is robust to outliers. ax.hist(x, bins='fd') applies the second one automatically.

Python· Edit the code and run it again

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(42)
heights = rng.normal(170, 8, 500)
k = int(np.ceil(np.log2(heights.size))) + 1
print('Sturges bins:', k)
print(f'mean = {heights.mean():.1f} cm, std = {heights.std(ddof=1):.1f} cm')

fig, ax = plt.subplots(figsize=(6, 4))
ax.hist(heights, bins=k, edgecolor='white')
ax.axvline(heights.mean(), color='red', linestyle='--', label='mean')
ax.set_xlabel('Height, cm')
ax.set_ylabel('Number of people')
ax.legend()
plt.show()

▸ Expected output

Sturges bins: 10
mean = 169.9 cm, std = 7.7 cm

Example 1: bins for the heights of 500 people

n = 500, the heights are roughly normal with σ ≈ 8 cm. Compute the bins with the Sturges and Freedman–Diaconis rules. For a normal distribution IQR ≈ 1.35σ.

Show solution

Sturges: log₂ 500 ≈ 8.97 → ⌈8.97⌉ = 9 → k = 9 + 1 = 10 bins (as in the code).
Freedman–Diaconis: IQR ≈ 1.35 · 8 = 10.8 cm; n^(1/3) = 500^(1/3) ≈ 7.94.
h = 2 · 10.8 / 7.94 ≈ 2.7 cm.
The range is about 170 ± 3σ, i.e. ~48 cm → 48 / 2.7 ≈ 18 bins.
FD shows finer detail; as n grows, Sturges adds bins very slowly.

fᵢ = nᵢ / (n · h) ∑ fᵢ · h = 1fᵢ = nᵢ / (n · h) ∑ fᵢ · h = 1

where:

nᵢobservations in bin i
fᵢbar height with density=True (density)
hbin width

ax.hist(x, density=True) makes the bar areas add up to 1 — such a histogram can be compared with a probability density curve.

Example 2: a density histogram

200 measurements are split into bins of width h = 2. One bin holds 30 measurements. What is the height of this bar with density=True? What does its area show?

Show solution

f = 30 / (200 · 2) = 0.075.
Area = f · h = 0.075 · 2 = 0.15, so 15% of the measurements are in this bin (30 / 200).
The areas of all bars add up to 1 (100%).

Several charts in one figure

plt.subplots(2, 2) returns a 2 × 2 array of Axes; you reach each chart with axes[row, col]. layout='constrained' keeps titles and axes from overlapping, and sharex=True makes the axes shared.

Python· Edit the code and run it again

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(0)
x = np.linspace(0, 2 * np.pi, 100)
fig, axes = plt.subplots(2, 2, figsize=(8, 6), layout='constrained')
axes[0, 0].plot(x, np.sin(x))
axes[0, 0].set_title('Line: sin x')
axes[0, 1].bar(['A', 'B', 'C'], [5, 3, 7])
axes[0, 1].set_title('Bar')
axes[1, 0].scatter(rng.random(30), rng.random(30))
axes[1, 0].set_title('Scatter')
axes[1, 1].hist(rng.normal(size=300), bins=15)
axes[1, 1].set_title('Histogram')
fig.suptitle('Four basic chart types')
print(axes.shape)
plt.show()

▸ Expected output

(2, 2)

pandas has its own .plot() method built on matplotlib: each DataFrame column becomes a series and the index goes on the X axis. The method returns an Axes, so you can finish the chart with ordinary matplotlib commands.

Python· Edit the code and run it again

import pandas as pd
import matplotlib.pyplot as plt

df = pd.DataFrame({'month': ['Jan', 'Feb', 'Mar'],
                   'Baku': [279, 153, 426],
                   'Ganja': [150, 306, 168]}).set_index('month')
ax = df.plot(kind='bar', figsize=(6, 3.5), rot=0, title='Revenue by month, AZN')
ax.set_ylabel('AZN')
print(df.sum())
plt.show()

▸ Expected output

Baku     858
Ganja    624
dtype: int64

Rules of a good chart

One chart, one idea. Put the conclusion in the title: “Baku branch leads in March”.
On a bar chart the Y axis must start at 0, because the eye compares bar lengths.
Make colours meaningful: give the series you want to highlight a bright colour and the rest grey.
Avoid 3D effects, shadows and pie charts with many slices — they distort values.

Python· Edit the code and run it again

import matplotlib.pyplot as plt

branches = ['Baku', 'Ganja']
satisfied = [96, 98]
fig, (bad, good) = plt.subplots(1, 2, figsize=(8, 3.5), layout='constrained')
bad.bar(branches, satisfied, color=['gray', 'orange'])
bad.set_ylim(95, 98.5)
bad.set_title('Misleading: axis starts at 95')
good.bar(branches, satisfied, color=['gray', 'orange'])
good.set_ylim(0, 100)
good.set_title('Honest: axis starts at 0')
for ax in (bad, good):
    ax.set_ylabel('Satisfied customers, %')
plt.show()

On the left, Ganja's bar looks three times longer than Baku's, although the difference is only 2 percentage points.

Exercise

Build a horizontal bar chart (ax.barh) from the revenue dictionary, set the title to 'Revenue by product' and label the X axis 'AZN'. Then print on separate lines: 1) the chart's title (ax.get_title()); 2) the number of bars on the chart (len(ax.patches)); 3) the product with the highest revenue.

Exercise · Python· Edit the code and run it again

import matplotlib.pyplot as plt

revenue = {'Coffee': 564, 'Cake': 540, 'Tea': 378, 'Juice': 212, 'Sandwich': 305}
fig, ax = plt.subplots()
# draw the bars, set the title and the X label, then print the three results

▸ Expected output

Revenue by product
5
Coffee

Exercise

Build a histogram of the test scores with 5 bins. ax.hist returns three things: the counts, the bin edges and the bars. Print on separate lines: 1) the count in each bin as a list of integers; 2) the width of one bin rounded to 2 decimal places.

Exercise · Python· Edit the code and run it again

import matplotlib.pyplot as plt

scores = [55, 62, 68, 70, 71, 75, 78, 80, 82, 85, 88, 90, 94, 97]
fig, ax = plt.subplots()
# counts, edges, _ = ax.hist(...)

▸ Expected output

[2, 3, 3, 3, 3]
8.4

Key points

The Figure is the whole image and an Axes is a chart inside it; start with fig, ax = plt.subplots().
Time → line, categories → bars, two numeric variables → scatter, distribution → histogram.
Every chart needs a title, axis labels with units and, when needed, a legend.
Bins: Sturges k = ⌈log₂ n⌉ + 1, Freedman–Diaconis h = 2 · IQR · n^(−1/3).
A bar chart's axis starts at 0; choose viridis for colour maps.

Check yourself

10 questions. Every correct answer earns XP.

1 / 10

Which chart is best for comparing the annual revenue of five branches?