Visualizing Data

Introduction

A good chart answers a question faster than a table of numbers. This lesson covers the four workhorse charts of data analysis: histograms, bar charts, box plots and scatter plots - what each is for, how to build it, and how to avoid the common traps.

Histogram: One Continuous Variable

A histogram bins a continuous variable and counts how many values fall in each bin. It shows the distribution's shape: center, spread, skewness, gaps, and outliers.

import matplotlib.pyplot as plt
import numpy as np
rng = np.random.default_rng(5)
values = rng.gamma(2.4, 2, 500)
plt.hist(values, bins=20, color="#2b6cb0", edgecolor="white")
plt.title("Histogram: distribution of one variable")
plt.xlabel("value"); plt.ylabel("count")
plt.tight_layout(); plt.show()

Guidelines:

• Choose bins so the shape is visible; 15-30 bins work for most datasets.
• Too few bins hide detail; too many create noise.

Bar Chart: Categorical Comparison

A bar chart compares counts or averages across categories. The bars are separated - do not connect them.

plt.bar(["Mon", "Tue", "Wed", "Thu", "Fri"], rng.integers(30, 90, 5), color="#e53e3e", alpha=0.9)
plt.title("Bar chart: categorical comparison")
plt.ylabel("count")
plt.tight_layout(); plt.show()

Box Plot: Compare Groups

A box plot summarizes a distribution with five numbers: min (fence), Q1, median, Q3, max (fence). It is the best chart for comparing several groups side by side.

groups = [rng.normal(50, 8, 120), rng.normal(60, 12, 120), rng.normal(45, 6, 120)]
plt.boxplot(groups, tick_labels=["A", "B", "C"], patch_artist=True)
plt.title("Box plot: compare groups")
plt.ylabel("score")
plt.tight_layout(); plt.show()

Read box plots like this:

• The box spans Q1 to Q3 (the middle 50%).
• The line inside the box is the median.
• Whiskers extend to the fences (1.5 x IQR).
• Dots beyond the whiskers are potential outliers.

Scatter Plot: Two Continuous Variables

A scatter plot shows the relationship between two continuous variables: direction, strength, and shape.

x = rng.normal(0, 1, 150)
y = 0.6 * x + rng.normal(0, 0.8, 150)
plt.scatter(x, y, s=22, alpha=0.7, color="#805ad5")
plt.title("Scatter plot: two variables")
plt.xlabel("x"); plt.ylabel("y")
plt.tight_layout(); plt.show()

Which Chart When?

Choosing Between Histogram and Box Plot

• Histogram: shows the full shape (skewness, gaps, multiple modes).
• Box plot: compact, great for comparing many groups, hides subtle shape.

Common Pitfalls

• Bar chart for continuous data (should be a histogram).
• Line chart for categorical, unordered data.
• 3D charts and pie charts for precise comparisons (humans read angles poorly).
• Colored charts with no legend or misleading axis starting points.

Summary

• Histogram = shape of one continuous variable.
• Bar chart = categorical comparison.
• Box plot = group comparison with robust summaries.
• Scatter plot = relationship between two continuous variables.
• Match the chart to the data type, and always label axes.

Next Lesson

Charts are great, but to reason about uncertainty you need probability. The next lesson introduces probability basics: events, rules, and the multiplication rule with conditional probability.