1. Definition of a Pie Chart

• A pie chart is a circular chart divided into sectors (slices), each representing a proportion of the whole.
• The entire pie represents 100% of the data, and each sector’s size is proportional to its share of the total.

2. Components of a Pie Chart

• Circle (Whole): Represents the total dataset or 100%.
• Sectors (Slices): Each sector represents a category, showing its proportion relative to the whole.
• Labels: Each sector may be labeled with the category name and its corresponding percentage or fraction of the whole.
• Legend: Explains the categories represented by each sector, often using colors or patterns.

3. Understanding Central Angles

• Central Angle: The angle formed at the center of the pie chart by two radii (lines from the center to the edge of the circle) that define a sector.
• The size of each central angle is directly proportional to the size of the sector and the proportion of the data it represents.
• Total Central Angles: The sum of all central angles in a pie chart is 360° because the chart is a complete circle.

4. Calculating Central Angles

To calculate the central angle for each sector:

1. Determine the Fraction or Percentage:
   • Identify the percentage or fraction of the total that each category represents.
2. Use the Formula:
   • Convert the percentage to a fraction (if needed) and multiply by 360°.
   • Formula: Central Angle (in degrees) = (Percentage/100) × 360°

5. Steps to Create a Pie Chart with Central Angles

1. Collect Data: Gather data and determine the percentage or fraction for each category.
2. Calculate Central Angles: Use the formula to calculate the central angle for each sector.
3. Draw the Circle: Draw a circle representing the entire dataset.
4. Draw Sectors: Starting from a fixed radius (like the 12 o’clock position), use a protractor to measure and draw each sector’s central angle.
5. Label Sectors: Label each sector with its category name and the corresponding percentage or fraction.
6. Add a Legend: Include a legend if necessary to clarify the categories.

6. Interpreting Pie Charts with Central Angles

• Visualizing Proportions: Larger central angles correspond to larger sectors, indicating a larger proportion of the data.
• Comparing Categories: By comparing the central angles or sector sizes, you can determine which categories are most or least significant

7. Examples and Practice

• Example 1: A pie chart representing time spent on daily activities.
  • Categories: Sleep , Schoo, Homework , Leisure , Others

8. Real-World Applications

• Business: Pie charts with central angles are used in business to represent market share, budget allocations, and survey results.
• Science: Used to visualize data distributions, such as species population, energy consumption, or resource allocation.

9. Common Mistakes to Avoid

• Incorrect Angle Calculation: Ensure accurate calculations to prevent misrepresentation of data.
• Overlapping Sectors: Ensure that the sum of the central angles equals 360° to avoid overlapping or gaps between sectors.

let’s practice!