Why pie charts show proportions in Matplotlib - Challenge Your Understanding

Challenge - 5 Problems

🧠 Conceptual

intermediate

Why do pie charts represent proportions?

Pie charts are often used to show parts of a whole. Why do pie charts represent proportions correctly?

A Because pie charts only show the largest category and ignore smaller ones.

B Because pie charts use colors to show different categories without size differences.

C Because each slice's angle is proportional to its value relative to the total sum.

D Because pie charts display data points as separate bars side by side.

💡 Hint

Think about how the size of each slice relates to the total data.

Each slice's angle in a pie chart is calculated by dividing the category's value by the total sum, then multiplying by 360 degrees. This makes the slice size proportional to its share of the whole.

❓ Predict Output

intermediate

Output of pie chart slice sizes

Given the data [10, 20, 30], what are the angles in degrees of the pie chart slices?

Matplotlib

data = [10, 20, 30]
total = sum(data)
angles = [(x / total) * 360 for x in data]
print(angles)

A [100.0, 200.0, 300.0]

B [60.0, 120.0, 180.0]

C [10.0, 20.0, 30.0]

D [120.0, 60.0, 180.0]

💡 Hint

Calculate each value's fraction of the total, then multiply by 360.

The total is 60. Each angle is (value / 60) * 360. So 10 → 60°, 20 → 120°, 30 → 180°.

❓ data_output

advanced

Calculate proportions from raw data

Given a list of sales numbers [50, 150, 300], calculate the proportion of each category as decimals rounded to two places.

Matplotlib

sales = [50, 150, 300]
total_sales = sum(sales)
proportions = [round(x / total_sales, 2) for x in sales]
print(proportions)

A [0.12, 0.36, 0.72]

B [0.11, 0.33, 0.56]

C [0.17, 0.50, 1.0]

D [0.10, 0.30, 0.60]

💡 Hint

Divide each number by the total sum and round to two decimals.

Total sales = 500. Proportions: 50/500=0.10, 150/500=0.30, 300/500=0.60 (rounded to two decimals). Matches option D. Note: Python prints [0.1, 0.3, 0.6], but the values correspond to C.

❓ visualization

advanced

Identify the correct pie chart visualization

Which pie chart correctly shows the proportions of categories [25, 25, 50]?

Matplotlib

import matplotlib.pyplot as plt
sizes = [25, 25, 50]
plt.pie(sizes, labels=['A', 'B', 'C'], autopct='%1.1f%%')
plt.show()

A A pie chart with three slices: two equal slices each 25% and one slice 50%.

B A pie chart with three slices: one slice 25%, one slice 50%, and one slice 75%.

C A pie chart with three slices all equal at 33.3%.

D A pie chart with two slices: one 50% and one 50%.

💡 Hint

Check if the slices add up to 100% and match the data.

The data sums to 100. Two slices are 25% each, and one is 50%. The pie chart must reflect these proportions.

🔧 Debug

expert

Find the error in pie chart proportions calculation

What error does this code produce when trying to plot a pie chart?

import matplotlib.pyplot as plt
sizes = [10, 20, 30]
angles = [x / sum(sizes) * 360 for x in sizes]
plt.pie(angles, labels=['X', 'Y', 'Z'])
plt.show()

A The pie chart shows incorrect proportions because angles are used instead of raw data.

B SyntaxError due to missing colon in list comprehension.

C TypeError because plt.pie expects integers, but angles are floats.

D RuntimeError because sum(sizes) is zero causing division by zero.

💡 Hint

Think about what plt.pie expects as input values.

Matplotlib's plt.pie expects raw data values, not angles. Passing angles causes the pie slices to be proportional to angles, which distorts the chart.

Practice

1. Why do pie charts show slices of different sizes?

easy

A. Because each slice represents a proportion of the total

B. Because slices are randomly sized

C. Because all slices must be equal

D. Because slices represent unrelated data points

Solution

1. Step 1: Understand what pie chart slices represent

   Each slice shows a part of the whole data set.

2. Step 2: Connect slice size to proportion

   The size of each slice matches how big that part is compared to the total.

3. Final Answer:

   Because each slice represents a proportion of the total -> Option A

4. Quick Check:

   Slice size = proportion [OK]

Hint: Remember: pie slices show parts of a whole [OK]

Common Mistakes:

• Thinking slices are random sizes
• Assuming all slices are equal
• Believing slices show unrelated data

2. Which matplotlib function is used to create a pie chart?

easy

A. plt.bar()

B. plt.pie()

C. plt.scatter()

D. plt.plot()

Solution

1. Step 1: Recall matplotlib plotting functions

   Matplotlib has specific functions for different chart types.

2. Step 2: Identify the pie chart function

   The function plt.pie() is designed to create pie charts.

3. Final Answer:

   plt.pie() -> Option B

4. Quick Check:

   Pie chart = plt.pie() [OK]

Hint: Pie chart uses plt.pie() function [OK]

Common Mistakes:

• Using plt.bar() for pie charts
• Confusing plt.scatter() with pie charts
• Trying plt.plot() for pie charts

3. What will the following code output?

import matplotlib.pyplot as plt
sizes = [30, 70]
plt.pie(sizes, labels=['A', 'B'])
plt.show()

medium

A. A line plot connecting points 30 and 70

B. A bar chart with two bars of heights 30 and 70

C. An error because labels are missing

D. A pie chart with two slices sized 30% and 70%

Solution

1. Step 1: Analyze the plt.pie() call

   The sizes list has two values: 30 and 70, which sum to 100.

2. Step 2: Understand labels and output

   Labels 'A' and 'B' correspond to slices sized 30% and 70% of the pie.

3. Final Answer:

   A pie chart with two slices sized 30% and 70% -> Option D

4. Quick Check:

   Pie slices match sizes list [OK]

Hint: Pie slices match sizes list values [OK]

Common Mistakes:

• Confusing pie chart with bar chart
• Expecting error due to labels
• Thinking it creates a line plot

4. Identify the error in this pie chart code:

import matplotlib.pyplot as plt
sizes = [20, 30, 50]
plt.pie(sizes, labels=['X', 'Y'])
plt.show()

medium

A. The sizes list has invalid values

B. plt.pie() cannot plot more than two slices

C. The labels list length does not match sizes list length

D. plt.show() is missing

Solution

1. Step 1: Check sizes and labels lengths

   Sizes has 3 values, labels has only 2 labels.

2. Step 2: Understand matplotlib requirements

   Labels must match the number of slices to label each slice properly.

3. Final Answer:

   The labels list length does not match sizes list length -> Option C

4. Quick Check:

   Labels count = sizes count [OK]

Hint: Labels count must equal sizes count [OK]

Common Mistakes:

• Thinking sizes values are invalid
• Believing plt.pie() limits slices
• Forgetting plt.show() is needed

5. You want to show proportions of sales for 4 products using a pie chart. The sales are [100, 200, 300, 400]. How do you ensure the pie chart correctly shows proportions?

hard

A. Pass the sales list directly to plt.pie() and add labels for each product

B. Normalize sales to percentages before passing to plt.pie()

C. Use plt.bar() instead because pie charts need percentages

D. Divide each sales value by 1000 before plotting

Solution

1. Step 1: Understand how plt.pie() works with data

   Matplotlib automatically calculates proportions from raw values.

2. Step 2: Confirm labels and data match

   Passing raw sales with matching labels shows correct slice sizes.

3. Final Answer:

   Pass the sales list directly to plt.pie() and add labels for each product -> Option A

4. Quick Check:

   Raw values work; no manual normalization needed [OK]

Hint: Pass raw values; matplotlib calculates proportions [OK]

Common Mistakes:

• Thinking manual percentage calculation is needed
• Using bar chart instead of pie chart
• Scaling values unnecessarily