Why pie charts show proportions in Matplotlib - Visual Breakdown

Concept Flow - Why pie charts show proportions

Start with data values

↓

Calculate total sum of values

↓

Calculate each value's proportion = value / total

↓

Convert proportions to angles for pie slices

↓

Draw pie chart slices with angles

↓

Display pie chart showing proportions

Pie charts show proportions by dividing each value by the total sum, converting these proportions into slice angles, and drawing slices accordingly.

Execution Sample

Matplotlib

import matplotlib.pyplot as plt
values = [10, 20, 30]
plt.pie(values, labels=['A', 'B', 'C'])
plt.show()

This code draws a pie chart with three slices sized by the values 10, 20, and 30.

Execution Table

Step	Action	Calculation	Result
1	Start with values	values = [10, 20, 30]	[10, 20, 30]
2	Calculate total sum	10 + 20 + 30	60
3	Calculate proportions	[10/60, 20/60, 30/60]	[0.1667, 0.3333, 0.5]
4	Convert proportions to angles	[0.1667*360, 0.3333*360, 0.5*360]	[60°, 120°, 180°]
5	Draw pie slices with angles	Slices sized 60°, 120°, 180°	Pie chart with 3 slices
6	Display pie chart	Show chart window	Pie chart visible on screen
7	End	All slices drawn	Execution complete

💡 All slices drawn, pie chart fully displayed

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	Final
values	[10, 20, 30]	[10, 20, 30]	[10, 20, 30]	[10, 20, 30]	[10, 20, 30]
total	N/A	60	60	60	60
proportions	N/A	N/A	[0.1667, 0.3333, 0.5]	[0.1667, 0.3333, 0.5]	[0.1667, 0.3333, 0.5]
angles	N/A	N/A	N/A	[60, 120, 180]	[60, 120, 180]

Key Moments - 3 Insights

Why do pie chart slices add up to a full circle?

Because each slice's angle is a proportion of the total sum, all slices together cover 360°, making a full circle. See execution_table step 4.

What happens if values are zero or negative?

Pie charts require positive values to show proportions correctly. Zero or negative values can cause errors or misleading slices. This is why values must be positive as in step 1.

Why do we divide each value by the total sum?

Dividing by the total converts raw values into proportions between 0 and 1, which represent parts of the whole. This is shown in step 3 of the execution_table.

Visual Quiz - 3 Questions

Look at the execution_table, what is the proportion of the second value after step 3?

A 0.3333

B 0.1667

C 0.5

D 1.0

💡 Hint

Check the 'proportions' calculation in step 3 of execution_table.

At which step do we convert proportions into angles for the pie slices?

A Step 3

B Step 4

C Step 2

D Step 5

💡 Hint

Look for the step mentioning 'Convert proportions to angles' in execution_table.

If the total sum was 100 instead of 60, how would the angles change?

A Angles would be smaller

B Angles would be larger

C Angles would stay the same

D Cannot tell from given data

💡 Hint

Angles depend on proportions, which remain the same if values scale proportionally. See variable_tracker for proportions.

Concept Snapshot

Pie charts show proportions by dividing each value by the total sum.
Each proportion is multiplied by 360° to get slice angles.
Slices are drawn with these angles to represent parts of the whole.
All slices together form a full circle (360°).
Values must be positive to display correctly.

Full Transcript

Pie charts visualize parts of a whole by showing slices sized according to proportions. We start with data values, calculate their total sum, then find each value's proportion by dividing by the total. These proportions are converted into angles by multiplying by 360 degrees. Each slice of the pie chart corresponds to one angle, so the whole pie sums to 360 degrees. This method ensures the chart visually represents how each value relates to the total. Positive values are required for meaningful slices. The code example uses matplotlib to draw a pie chart with three slices sized by values 10, 20, and 30.

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