To solve this problem, we need to calculate the relative frequencies as percentages and then create a pie chart.

Step 1: Calculate the total frequency

The total frequency is the sum of all the frequencies provided: $\text{Total Frequency} = 2 + 8 + 10 + 4 = 24$

Step 2: Compute the relative frequency for each grade

The relative frequency as a percentage is calculated as: $\text{Relative Frequency (\%)} = \left( \frac{\text{Frequency of a grade}}{\text{Total Frequency}} \right) \times 100$

• Grade A: $\text{Relative Frequency} = \left( \frac{2}{24} \right) \times 100 = 8.33\%$

• Grade B: $\text{Relative Frequency} = \left( \frac{8}{24} \right) \times 100 = 33.33\%$

• Grade C: $\text{Relative Frequency} = \left( \frac{10}{24} \right) \times 100 = 41.67\%$

• Grade F: $\text{Relative Frequency} = \left( \frac{4}{24} \right) \times 100 = 16.67\%$

Step 3: Tabulate the results

The completed table looks like this:

Step 4: Create the pie chart

Each percentage corresponds to an angle in the pie chart: $\text{Angle} = \left( \text{Relative Frequency (\%)} \right) \times \frac{360}{100}$

• Grade A: $8.33 \times 3.6 = 30\degree$
• Grade B: $33.33 \times 3.6 = 120\degree$
• Grade C: $41.67 \times 3.6 = 150\degree$
• Grade F: $16.67 \times 3.6 = 60\degree$

I will now generate a labeled pie chart based on this data. matplotlib.pyplot as plt

Data for the pie chart

labels = ['A (8.33%)', 'B (33.33%)', 'C (41.67%)', 'F (16.67%)'] sizes = [8.33, 33.33, 41.67, 16.67] colors = ['gold', 'lightblue', 'lightgreen', 'salmon'] explode = (0.1, 0, 0, 0) # Slightly explode the first slice for emphasis

Create the pie chart

plt.figure(figsize=(8, 8)) plt.pie(sizes, labels=labels, colors=colors, explode=explode, autopct='%1.1f%%', startangle=140) plt.title('Distribution of Grades') plt.axis('equal') # Equal aspect ratio ensures the pie chart is circular. plt.show()Here is the completed pie chart showing the distribution of grades. Each slice is labeled with the grade and its relative percentage for clarity.

Would you like further details or have any questions? Here are some related questions for you:

1. How can we use relative frequencies in statistical analysis?
2. Why is it important to represent data visually, such as with a pie chart?
3. Can you explain when to use a pie chart versus other types of charts?
4. How would you calculate cumulative frequencies from this data?
5. What other real-world examples might use a similar frequency analysis?

Tip: Always double-check the total frequency sum when calculating relative percentages to avoid errors in proportions!