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Chapter 4 · Solutions

Practice Challenges, Worked Answers ✅

Full solutions to the four "Types of Data & Variables" 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
NAVY="#0a1230"; INK="#1a2138"; INK_SOFT="#4a5578"
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.linewidth":1.2,"axes.grid":True,"grid.color":GRID,"axes.axisbelow":True,
    "axes.spines.top":False,"axes.spines.right":False,"axes.titlesize":14,"axes.titleweight":"bold","axes.titlecolor":INK,
    "axes.labelcolor":INK_SOFT,"xtick.color":INK_SOFT,"ytick.color":INK_SOFT,"legend.frameon":False})
print("✅ Ready.")

✅ Ready.

CHALLENGE 1 · CLASSIFY

Name each variable's type

For each variable, give the big type (qualitative/quantitative) and subtype (nominal/ordinal/discrete/continuous): age, eye color, number of siblings, temperature, T-shirt size (S/M/L).

answer = pd.DataFrame({
    "variable":["age","eye color","number of siblings","temperature","T-shirt size"],
    "big type":["Quantitative","Qualitative","Quantitative","Quantitative","Qualitative"],
    "subtype": ["Continuous","Nominal","Discrete","Continuous","Ordinal"],
    "why":     ["measured, any value","categories, no order","counted whole numbers",
                "measured, any value","categories WITH an order S<M<L"],
})
answer

	variable	big type	subtype	why
0	age	Quantitative	Continuous	measured, any value
1	eye color	Qualitative	Nominal	categories, no order
2	number of siblings	Quantitative	Discrete	counted whole numbers
3	temperature	Quantitative	Continuous	measured, any value
4	T-shirt size	Qualitative	Ordinal	categories WITH an order S<M<L

Answer: the trick is two questions, is it a number you can do math on? (quantitative vs qualitative), then countable or measurable? / ordered or not? T-shirt size is the classic "looks like a category but has order" → ordinal.

CHALLENGE 2 · SPLIT THE COLUMNS

Separate qualitative from quantitative

Given this customer table, list which columns are qualitative and which are quantitative.

customers = pd.DataFrame({
    "city":      ["Lagos","Cairo","Lagos","Nairobi"],
    "age":       [25, 41, 33, 29],
    "plan":      ["Free","Pro","Pro","Free"],
    "monthly_$": [0.0, 12.99, 12.99, 0.0],
})
qualitative  = [c for c in customers.columns if customers[c].dtype == "object"]
quantitative = [c for c in customers.columns if customers[c].dtype != "object"]
print("Qualitative  (categories):", qualitative)
print("Quantitative (numbers)   :", quantitative)

Qualitative  (categories): []
Quantitative (numbers)   : ['city', 'age', 'plan', 'monthly_$']

Answer: Qualitative → city, plan (text categories). Quantitative → age, monthly_$ (numbers). A quick first pass: pandas stores text categories as the object dtype.

CHALLENGE 3 · DISCRETE OR CONTINUOUS

Decide for each

Label each as discrete or continuous: cars in a parking lot, weight of a parcel, goals scored in a match, time to run 5 km.

items = {
    "cars in a parking lot": "Discrete (counted, whole numbers)",
    "weight of a parcel":    "Continuous (measured, any value)",
    "goals scored":          "Discrete (counted, whole numbers)",
    "time to run 5 km":      "Continuous (measured, any value)",
}
for k, v in items.items():
    print(f"{k:<24} -> {v}")

cars in a parking lot    -> Discrete (counted, whole numbers)
weight of a parcel       -> Continuous (measured, any value)
goals scored             -> Discrete (counted, whole numbers)
time to run 5 km         -> Continuous (measured, any value)

Answer: if you count it (cars, goals) it's discrete; if you measure it (weight, time) it's continuous. A handy test: continuous values can always have more decimal places.

CHALLENGE 4 · VARIABLE ROLES

Find IV, DV, and a confounder

Study: "Does the amount of fertilizer affect plant height?" Identify the independent variable, the dependent variable, and one possible confounder.

roles = {
    "Independent variable (cause)": "amount of fertilizer",
    "Dependent variable (effect)":  "plant height",
    "Possible confounder":          "sunlight (affects growth AND may vary by plot)",
}
for k, v in roles.items():
    print(f"{k:<32}: {v}")

Independent variable (cause)    : amount of fertilizer
Dependent variable (effect)     : plant height
Possible confounder             : sunlight (affects growth AND may vary by plot)

Answer: IV = fertilizer (what we change), DV = plant height (what we measure). A confounder like sunlight or watering could influence height too, so a fair experiment must hold those constant. IV → DV, with confounders controlled.

---

🎉 Nicely done!

You classified variables, split qualitative from quantitative, told discrete from continuous, and identified cause, effect, and a confounder, the vocabulary every later chapter assumes.

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

←Back to the bookChapter 4 · Take the quiz & aim for 100%