About Data Handling Ex 5.2 | CBSE Class 8 Maths

What is a Pie Chart?

A pie chart (or a circle graph) is a circular statistical graphic, which is divided into slices or sectors to illustrate numerical proportion. In a pie chart, the arc length of each slice, and consequently its central angle and area, is proportional to the quantity it represents. Think of it as a whole pizza (the circle) representing your total data. Each slice represents a category or a part of that total. The bigger the slice, the larger the proportion of data it represents. The entire circle always adds up to 100% of the data, and the sum of all the angles in the center of the circle is always 360 degrees. This visual representation makes it very easy to compare the parts among themselves and to the whole.

Step-by-Step: How to Draw a Pie Chart

1. Step 1: Find the Total and Calculate Fractions — First, add up all the values in your data to find the total. Then, for each category, find what fraction of the total it represents. The formula is: Fraction = (Value of the item) / (Total value).
2. Step 2: Calculate the Central Angle for Each Category — A full circle is 360°. To find the angle for each slice of the pie, multiply the fraction you calculated in Step 1 by 360°. The formula is: Central Angle = Fraction × 360°.
3. Step 3: Draw the Circle and First Radius — Use a compass to draw a neat circle. Mark the center and draw a straight line from the center to the edge of the circle (this is the first radius).
4. Step 4: Draw the Sectors — Place your protractor on the first radius with its center at the center of the circle. Measure the first angle you calculated and mark it. Draw a line from the center to this mark. This is your first sector. Now, use this new line as your base to measure and draw the next angle. Repeat until all sectors are drawn.
5. Step 5: Label Your Pie Chart — Label each sector with the name of the category it represents. You can also write the percentage or the actual value inside or next to the slice. Don't forget to give your pie chart a suitable title!

Worked Example: Reading a Pie Chart

• A survey was done on the favourite colours of 40 students. The results are shown in a pie chart where the central angles are: Blue (180°), Green (90°), Red (60°), and Yellow (30°). Question: How many students like the colour Red? Solution: Step 1: Find the fraction for Red. The angle for Red is 60°. The total angle is 360°. So, the fraction is 60/360 = 1/6. Step 2: Calculate the number of students. The total number of students is 40. Number of students who like Red = (Fraction for Red) × (Total students) = (1/6) × 40 = 40/6 ≈ 6.67. Since we can't have a fraction of a student, let's assume the total students were 36 for easier calculation in this example. Let's re-calculate with 36 students. Revised Example: Total students = 36. Number of students who like Red = (60/360) × 36 = (1/6) × 36 = 6 students. Final Answer: 6 students like the colour Red.

Exam Tip: The Central Angle is Key!

Remember this golden rule for your exams: The most crucial step in creating a pie chart is calculating the central angle correctly. A small mistake here will make your entire chart wrong. Always double-check your calculations.

The formula is: Central Angle = (Value of the Component / Total Value) × 360°

Also, a great way to check your work is to add up all the central angles you've calculated. They MUST sum up to exactly 360°. If they don't, you've made a mistake in your calculations and need to go back and find it.

Practice Questions with Solutions

• Q: The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart. Language: Hindi, English, Marathi, Tamil, Bengali No. of students: 40, 12, 9, 7, 4 A: Step 1: Find the total number of students. Total = 40 + 12 + 9 + 7 + 4 = 72 students. Step 2: Calculate the central angle for each language. - Hindi: (40/72) × 360° = 200° - English: (12/72) × 360° = 60° - Marathi: (9/72) × 360° = 45° - Tamil: (7/72) × 360° = 35° - Bengali: (4/72) × 360° = 20° (Check: 200+60+45+35+20 = 360°) Step 3: Draw a circle and use a protractor to draw sectors with the calculated angles. Final answer: A pie chart with sectors of 200°, 60°, 45°, 35°, and 20° representing Hindi, English, Marathi, Tamil, and Bengali respectively.
• Q: A pie chart shows the monthly expenditure of a family. The angle for 'Food' is 120°. If the total monthly income is ₹36,000, how much is spent on Food? A: Step 1: Identify the central angle for Food and the total angle in a circle. Angle for Food = 120°. Total angle = 360°. Step 2: Find the fraction of expenditure on Food. Fraction = 120°/360° = 1/3. Step 3: Calculate the amount spent on Food by multiplying the fraction by the total income. Amount on Food = (1/3) × ₹36,000 = ₹12,000. Final answer: The family spends ₹12,000 on Food.
• Q: On a particular day, the sales (in Rupees) of different items of a baker’s shop are given below. Ordinary Bread: 320, Fruit Bread: 80, Cakes: 160, Biscuits: 120, Others: 40. Draw a pie chart for this data. A: Step 1: Find the total sales. Total Sales = 320 + 80 + 160 + 120 + 40 = ₹720. Step 2: Calculate the central angle for each item. - Ordinary Bread: (320/720) × 360° = 160° - Fruit Bread: (80/720) × 360° = 40° - Cakes: (160/720) × 360° = 80° - Biscuits: (120/720) × 360° = 60° - Others: (40/720) × 360° = 20° (Check: 160+40+80+60+20 = 360°) Step 3: Draw a circle and draw the sectors with the calculated angles, labeling each one. Final answer: A pie chart with sectors of 160°, 40°, 80°, 60°, and 20° representing the sales of different bakery items.
• Q: A survey of 120 people found that 50% liked watching cricket, 30% liked football, and 20% liked tennis. Calculate the central angle for each sport. A: Step 1: Convert percentages to values. The total is 360°. We can directly calculate the angle from the percentage. Angle = Percentage × 360°. Step 2: Calculate the angle for each sport. - Cricket: 50% of 360° = (50/100) × 360° = 180° - Football: 30% of 360° = (30/100) × 360° = 108° - Tennis: 20% of 360° = (20/100) × 360° = 72° (Check: 180° + 108° + 72° = 360°) Final answer: The central angles are 180° for Cricket, 108° for Football, and 72° for Tennis.

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