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.