This lesson focuses on a key method for visually representing data: the pie chart. Pie charts are used to show how a total amount is divided into different parts or categories. You will learn both how to draw a pie chart from a set of data and how to interpret information from a given pie chart.

1. Core Concepts (Short Notes)

• Pie Chart: A circular graph that is divided into sectors to illustrate numerical proportion.

• The Whole Circle: Represents the total amount of all the data combined (e.g., total number of students, total budget).

• Total Angle: The angle around the centre of any circle is 360°. This is the most important number in this topic.

• Sectors: Each "slice" of the pie is a sector. The size of each sector is proportional to the quantity it represents. The size is determined by its angle at the centre.

2. Key Methods & Formulas

A) Drawing a Pie Chart (From Data to Angles)

To draw a pie chart, you must convert each data value into an angle.

Main Formula: Angle of Sector = (Value for the category / Total Value of all data) × 360°

Step-by-Step Guide:

1. Find the Total: Add up all the data values to find the total amount.

2. Calculate the Angle for Each Category: Use the formula above for each individual category.

3. Check Your Angles: Crucial Step! The sum of all your calculated sector angles must equal 360°. If it doesn't, you've made a calculation error.

4. Draw the Chart:

   • Use a compass to draw a circle.

   • Draw a radius to act as your starting line.

   • Use a protractor to measure and draw the first sector's angle.

   • From the new line you just drew, measure and draw the next angle. Repeat for all sectors.

5. Label Everything: Clearly label what each sector represents. You can also use a color-coded key.

B) Interpreting a Pie Chart (From Angles to Data)

To find the actual value a sector represents, you work backwards.

Main Formula: Value for the category = (Angle of Sector / 360°) × Total Value

3. Tips & Tricks for Exams

• Look for Easy Numbers: Often, the "Total Value" in an exam question will be a factor of 360 (like 60, 90, 120, 180). This makes the calculation 360 / Total a simple whole number, which is the "degrees per unit of data".

  • Example: If the total number of students is 90, then each student is represented by 360° / 90 = 4°. A group of 15 students would then have an angle of 15 × 4° = 60°.

• Working with Percentages: If the data is given in percentages, the "Total Value" is 100.

  • Angle of Sector = (Percentage / 100) × 360°

• Comparing Sectors: You can compare the sizes of different categories just by looking at their angles, without needing the total value.

  • A sector with an angle of 120° represents twice the amount of a sector with an angle of 60°.

4. Important Points to Remember

• The Magic Number is 360: Every calculation in this topic revolves around the 360 degrees in a circle.

• Protractor Accuracy: When drawing, be as accurate as possible with your protractor. Place the center point carefully.

• Don't Forget the "Remaining" Category: Sometimes a question will list several categories and say "the rest...". You must first calculate the value of "the rest" before you can find its angle.

• Units: Make sure your final answers have the correct units (e.g., "students", "Rs.", "hectares").