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Chapter 14 · Solutions

Practice Challenges, Worked Answers ✅

Full solutions to the five "Charts for Categorical Data" challenges. Try them yourself first, then compare.

Statistics, Data Science and AI: A Visual Handbook · John Fisher · 2026

⚙️ Setup

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

INK="#1a2138"; CYAN="#0891b2"; PURPLE="#7c3aed"; AMBER="#d97706"; GREEN="#059669"; PINK="#db2777"; BLUE="#2563eb"; GRID="#e6e9f2"
plt.rcParams.update({"figure.facecolor":"white","axes.facecolor":"white","figure.dpi":110,"font.size":11,
   "axes.edgecolor":GRID,"axes.grid":True,"grid.color":GRID,"axes.axisbelow":True,"axes.spines.top":False,
   "axes.spines.right":False,"axes.titlesize":12,"axes.titleweight":"bold","legend.frameon":False})
print("Ready.")

Ready.

CHALLENGE 1 · SORTED BARS

Build the right bar chart

From the pet counts below, draw a horizontal bar chart sorted by value. Why is horizontal + sorted a good choice here?

pets = pd.Series({"Dog":48,"Cat":39,"Fish":12,"Rabbit":7,"Reptile":5,"Bird":15})
pets = pets.sort_values()
fig, ax = plt.subplots(figsize=(7,4))
ax.barh(pets.index, pets.values, color=CYAN, edgecolor="white", height=0.7)
ax.set_xlabel("count"); ax.set_title("Pets owned"); ax.grid(axis="y", visible=False)
for i,v in enumerate(pets.values): ax.text(v+0.5, i, str(v), va="center", fontweight="bold")
plt.tight_layout(); plt.show()

Answer: Sorting makes the ranking instant, and horizontal bars give each label room without rotating text. These are nominal categories (no natural order), so reordering by value is perfectly fair, that would NOT be allowed for ordinal categories like S/M/L/XL.

CHALLENGE 2 · SPOT THE LIE

Fix a misleading axis

A chart compares two satisfaction scores, 82 and 86, with the y-axis starting at 80. Redraw it honestly and quantify how much the truncated axis exaggerates the gap.

labels=["Team A","Team B"]; vals=[82, 86]
fig,(a1,a2)=plt.subplots(1,2,figsize=(10,4))
a1.bar(labels, vals, color=PINK, edgecolor="white", width=0.6); a1.set_ylim(80,88)
a1.set_title("Truncated (starts at 80)")
a2.bar(labels, vals, color=GREEN, edgecolor="white", width=0.6); a2.set_ylim(0,100)
a2.set_title("Zero baseline (honest)")
plt.tight_layout(); plt.show()
looks=(vals[1]-80)/(vals[0]-80); real=vals[1]/vals[0]
print(f"truncated bar heights ratio: {looks:.1f}x   |   real ratio: {real:.2f}x")

truncated bar heights ratio: 3.0x   |   real ratio: 1.05x

Answer: Starting at 80 makes Team B's bar look 3x Team A's, when the scores really differ by under 5%. Because a bar encodes length from zero, cutting the baseline breaks that proportionality. The honest fix is a zero baseline (or, if zero is impractical, switch to a dot plot, which does not require one).

CHALLENGE 3 · BAR OR HISTOGRAM?

Tell them apart

For each dataset, say whether you would draw a bar chart or a histogram, and what the visual tell is: (a) counts of favorite ice-cream flavor; (b) the distribution of 500 customers' ages.

print("(a) favorite flavor  -> BAR CHART  : distinct categories, bars have GAPS, reorderable")
print("(b) ages of 500 people -> HISTOGRAM : continuous values binned, bars TOUCH, fixed order")

(a) favorite flavor  -> BAR CHART  : distinct categories, bars have GAPS, reorderable
(b) ages of 500 people -> HISTOGRAM : continuous values binned, bars TOUCH, fixed order

Answer: (a) Flavor is categorical, so a bar chart with gaps between bars; you may sort them. (b) Age is continuous, so a histogram of binned ages with touching bars along a number line, and the bins stay in numeric order. The touching-vs-gapped bars are the quickest tell.

CHALLENGE 4 · PIE TO BAR

When a pie fails

A survey of 8 favorite-genre categories is shown as a pie chart and readers cannot rank the middle ones. Convert it to a sorted bar chart and explain why the bar is clearer.

genre = pd.Series({"Pop":21,"Rock":18,"Hip-Hop":17,"Country":12,"Jazz":11,"EDM":9,"Classical":7,"Other":5})
g = genre.sort_values()
fig, ax = plt.subplots(figsize=(7.5,4.2))
ax.barh(g.index, g.values, color=PURPLE, edgecolor="white", height=0.7)
ax.set_xlabel("share (%)"); ax.set_title("Favorite genre (sorted)"); ax.grid(axis="y", visible=False)
for i,v in enumerate(g.values): ax.text(v+0.3, i, f"{v}%", va="center", fontweight="bold")
plt.tight_layout(); plt.show()
print(f"slices sum to {genre.sum()}%")

slices sum to 100%

Answer: Eight slices is far too many for a pie, several are near the same size and the eye cannot rank angles that close. On a sorted bar chart every value sits on a common scale, so the ranking and the near-ties (Rock 18 vs Hip-Hop 17) are obvious. As a rule, keep pies to about 5 slices at most; otherwise use a bar.

CHALLENGE 5 · GROUPED VS STACKED

Pick the layout for the question

You have sales of two product lines across three regions. Make BOTH a grouped and a stacked bar chart, then say which answers "which line sells more in each region?" and which answers "what is each region's total?"

regions=["North","South","West"]; line1=np.array([40,55,30]); line2=np.array([25,20,45])
x=np.arange(3); w=0.38
fig,(a1,a2)=plt.subplots(1,2,figsize=(12,4.2))
a1.bar(x-w/2,line1,w,label="Line 1",color=CYAN,edgecolor="white")
a1.bar(x+w/2,line2,w,label="Line 2",color=AMBER,edgecolor="white")
a1.set_title("Grouped"); a1.set_xticks(x); a1.set_xticklabels(regions); a1.legend()
a2.bar(x,line1,label="Line 1",color=CYAN,edgecolor="white")
a2.bar(x,line2,bottom=line1,label="Line 2",color=AMBER,edgecolor="white")
a2.set_title("Stacked"); a2.set_xticks(x); a2.set_xticklabels(regions); a2.legend()
plt.tight_layout(); plt.show()

Answer: The grouped chart answers "which line sells more in each region?" because both bars share the zero baseline and compare directly. The stacked chart answers "what is each region's total?" because the segments add up to the full height, but the upper (Line 2) segments float, so comparing Line 2 across regions on the stacked chart is hard. Match the layout to the question.

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🎉 Nicely done!

You built honest bar charts, exposed a truncated-axis lie, separated bars from histograms, retired an overloaded pie, and matched grouped vs stacked layouts to the question being asked. A chart is an argument, you can now make yours clearly and fairly.

Statistics, Data Science and AI: A Visual Handbook · © 2026 John Fisher

←Back to the bookChapter 14 · Take the quiz & aim for 100%