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4.2.1 - Drawing pie charts

Interactive Audio Lesson

Listen to a student-teacher conversation explaining the topic in a relatable way.

Introduction to Pie Charts

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Teacher
Teacher

Today, we will learn about pie charts, also known as circle graphs. Can anyone tell me why we use pie charts?

Student 1
Student 1

To show parts of a whole, like percentages!

Teacher
Teacher

Exactly! Pie charts visually represent data by dividing a circle into sectors. Each sector shows the proportion of each category compared to the total. Remember, the full circle equals 360 degrees.

Student 2
Student 2

How do we calculate the angle for each sector?

Teacher
Teacher

Great question! We'll calculate the central angle by taking the percentage of each category and multiplying it by 360 degrees. For example, if 50% of students prefer chocolate ice cream, what would the angle be?

Student 3
Student 3

That would be 180 degrees!

Teacher
Teacher

Perfect! Now, let's summarize: Pie charts show relationships between parts and a whole, and we find angles by multiplying percentages by 360 degrees.

Drawing a Pie Chart Step by Step

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Teacher
Teacher

Now that we know how to calculate angles, let's talk about drawing a pie chart. First, we need to have our data ready. Let’s say we've surveyed students about ice cream flavors. Who wants to help me with that?

Student 4
Student 4

I have the data! Chocolate 50%, Vanilla 25%, Other flavors 25%.

Teacher
Teacher

Awesome! We can put this into a table to visualize our calculations. Who can tell me the angle for Vanilla?

Student 1
Student 1

That's 90 degrees since 25% of 360 is 90!

Teacher
Teacher

First, draw a circle and mark the center. Use a protractor to measure 180 degrees for Chocolate.

Student 3
Student 3

Then we do that for Vanilla and Others?

Teacher
Teacher

Yes! Keep measuring and marking until we complete our pie chart. Let’s recap this step: Calculate, table, draw!

Practice Drawing Pie Charts

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Teacher
Teacher

Now that you understand how to draw pie charts, let’s practice. Here’s a new dataset: TV program watch preferences. I'll give you the percentages.

Student 2
Student 2

What's the dataset?

Teacher
Teacher

Alright, here it is: Documentaries 30%, Sports 40%, News 30%. Calculate the angles and draw your pie charts.

Student 4
Student 4

For Sports that's 144 degrees, right?

Teacher
Teacher

Yes! How did you calculate that?

Student 4
Student 4

I multiplied 40% by 360 degrees.

Teacher
Teacher

Perfect! Let’s summarize our calculation: Documentaries: 108°, Sports: 144°, News: 108°. Now get to drawing!

Review and Application

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Teacher
Teacher

Let’s discuss where you might see pie charts in real life. Who can name a place?

Student 1
Student 1

Businesses use them for sales data!

Student 2
Student 2

And in surveys to show results!

Teacher
Teacher

Exactly! Remember, pie charts make it easy to compare parts of a whole visually. Let’s recap: Pie charts shows relationships, calculate angles from percentages, and are used in many fields!

Student 3
Student 3

Do we always need to use percentages for pie charts?

Teacher
Teacher

Good question! Yes, pie charts effectively display parts of a whole, typically in percentages. You all did great today!

Introduction & Overview

Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.

Quick Overview

This section explains how to represent data using pie charts, illustrating the relationship between a whole and its parts through graphical representation.

Standard

Pie charts, also known as circle graphs, exemplify data representation in a circular form to depict the parts of a whole. This section covers how to calculate the central angle for each sector based on given data and provides detailed steps for drawing pie charts.

Detailed

Detailed Summary

The section focuses on drawing pie charts as a method of data representation. Pie charts, or circle graphs, showcase the relationship between a whole and its parts, effectively visualizing percentages or portions of different categories. For instance, if a survey reveals that 50% of students prefer chocolate ice cream, the corresponding pie chart sector for chocolate would occupy half the total angle of the circle, which is 180 degrees out of 360 degrees.

To illustrate this, the section provides a systematic approach to finding the central angle for each category based on its percentage representation. For example:

  • Calculate Central Angle: Multiply the percentage of each category by 360° to find the angle of each sector.
  • A table summarizing flavors and percentages aids students in visualizing this concept:
  • Chocolate: 50% = 180°
  • Vanilla: 25% = 90°
  • Other flavors: 25% = 90°

The text instructs students to draw a circle, mark its center, and use a protractor to accurately construct each sector according to calculated angles. Several examples reinforce the concept by presenting real data, such as the type of programs watched on TV or flavors of ice cream preferred by students, allowing them to practice drawing pie charts themselves.

Similar Questions

  1. On a certain day, the sales (in dollars) of different kinds of fruits at a market are provided below.
Item Sales (in Dollars)
Apples 150
Bananas 230
Grapes 120
Oranges 100
Other Fruits 200
Total 900

Create a pie chart from this data.

  1. On a specific day, the revenue (in euros) from a bookstore's sales of various book genres is shown below.
Genre Revenue (in Euros)
Fiction 250
Non-Fiction 180
Science 100
Fantasy 90
Other Genres 280
Total 900

Draw a pie chart based on the information provided.

  1. On a given day, the sales (in yen) of different types of beverages at a cafe are outlined below.
Beverage Sales (in Yen)
Coffee 400
Tea 300
Juice 200
Soft Drinks 100
Other Beverages 0
Total 1000

Illustrate a pie chart for this sales data.

  1. On a certain day, the expenditures (in pounds) for different categories of a household's budget are presented below.
Category Expenditure (in Pounds)
Rent 600
Groceries 150
Utilities 100
Transportation 50
Entertainment 100
Total 1000

Create a pie chart that represents this data.

  1. On a particular day, the sales (in rupees) of various types of clothing at a boutique are given below.
Item Sales (in Rupees)
Shirts 200
Pants 300
Jackets 150
Accessories 50
Other Clothing 150
Total 850

Draw a pie chart for the data provided.

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Audio Book

Dive deep into the subject with an immersive audiobook experience.

Understanding Percentages and Flavours

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The favourite flavours of ice-creams for students of a school is given in percentages as follows:

Flavours Percentage of students Preferring the flavours
Chocolate 50%
Vanilla 25%
Other flavours 25%

Detailed Explanation

In this chunk, we start by identifying the favorite ice cream flavours among students and their respective preferences listed in percentages. Chocolate is the most preferred flavour with 50%, followed by Vanilla and other flavours, each with 25%. Percentages provide a clear insight into how many students prefer each flavour in relation to the total number.

Examples & Analogies

Think of a birthday party where you ask your friends which ice cream flavour they want. If half of them say chocolate, it means chocolate is the most popular – similar to how we present this data in a pie chart.

Calculating Central Angles

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The total angle at the centre of a circle is 360°. The central angle of the sectors will be a fraction of 360°. We make a table to find the central angle of the sectors (Table 4.1).

Table 4.1
Flavours | Students in percent | In fractions | Fraction of 360°
--- | --- | --- | ---
Chocolate | 50 | 1/2 | 180°
Vanilla | 25 | 1/4 | 90°
Other flavours | 25 | 1/4 | 90°

Detailed Explanation

This chunk explains how we convert the percentages into angles for the pie chart. Since a circle has 360°, we multiply the percentage of each flavour by 360° to find the angle of each sector. For instance, Chocolate is 50% of the total, resulting in a central angle of 180° (half of the circle).

Examples & Analogies

Imagine you’re sharing a pizza with friends. If 50% of the pizza is cheese, you would take half the pizza for the cheese lovers! The same concept applies here when we translate preferences into angles on a pie chart.

Drawing the Pie Chart

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  1. Draw a circle with any convenient radius.
  2. Mark its center (O) and a radius (OA).
  3. The angle of the sector for chocolate is 180°. Use the protractor to draw ∠AOB = 180°.
  4. Continue marking the remaining sectors.

Detailed Explanation

Once we calculate the angles, the next step is to visually represent them. Begin by drawing a circle. Use a protractor to accurately measure and draw the angles for each flavour, ensuring their sizes correspond to the calculated angles: Chocolate gets 180°, Vanilla gets 90°, and so forth.

Examples & Analogies

Consider decorating a cake where each slice represents a different flavour. You need to draw clear lines to show how much of each flavour is on the cake, just like how we draw the sectors in a pie chart to represent data clearly.

Examples of Pie Charts

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Example 1: The adjoining pie chart gives the expenditure (in percentage) on various items and savings of a family during a month.
(i) On which item, the expenditure was maximum?
(ii) Expenditure on which item is equal to the total savings of the family?

Detailed Explanation

In this chunk, we discuss practical applications of pie charts through examples. The pie chart visually summarizes data on expenditures, allowing us to quickly see which items cost the most and how savings compare to spending. This makes it easier to analyze financial habits.

Examples & Analogies

Picture planning your monthly budget. You can see at a glance where your money goes and identify areas where you might need to cut back – just like the pie chart helps visualize spending habits of a family.

Another Example of a Pie Chart

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Example 2: 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 and pastries: 160
biscuits: 120
others: 40
Total: 720
Solution: We find the central angle of each sector.

Detailed Explanation

This chunk illustrates how pie charts can also represent sales data. By breaking down total sales into specific items, we find the angles for the respective sectors based on their sales proportion. This helps the bakery understand which products are selling best.

Examples & Analogies

Think of this as knowing which bakery item is the favorite among your friends. If everyone prefers ordinary bread, you'd want to make more of it the next time – just like the bakery uses pie charts to determine which products to promote.

Practical Exercise

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TRY THESE
Draw a pie chart of the data given below.
The time spent by a child during a day.
Sleep — 8 hours
School — 6 hours
Homework — 4 hours
Play — 4 hours
Others — 2 hours

Detailed Explanation

In this practical exercise, students are asked to create a pie chart based on daily activities. This reinforces the concept by allowing students to apply their knowledge of calculating angles and drawing pie charts with their own data.

Examples & Analogies

Consider this as creating a visual schedule for your day, where each activity takes up a portion of your time. This helps you see where you spend the most time and if you need to adjust your daily routine.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Pie Chart: A visual representation of data where a circle is divided into sectors.

  • Central Angle Calculation: Multiply the percentage of a category by 360° to determine the size of the sector it will represent in the pie chart.

  • Data Visualization: Using graphs like pie charts makes it easier to compare different parts of a whole.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • If a class consists of 100 students, and 50% prefer chocolate ice cream, the corresponding sector in the pie chart will represent 180 degrees.

  • In a survey where 60% of respondents prefer action movies, that sector would be 216 degrees in the pie chart.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • A pie chart's a playful sight, shows data parts with all its might.

📖 Fascinating Stories

  • Imagine a pizza divided among friends, each slice represents their favorite flavor, just like pie charts represent different data parts!

🧠 Other Memory Gems

  • To remember the pie chart steps: 'Calculate, Draw, Fit, Proportions!'

🎯 Super Acronyms

P.I.E.

  • Percentages into Every sector.

Flash Cards

Review key concepts with flashcards.

Glossary of Terms

Review the Definitions for terms.

  • Term: Pie Chart

    Definition:

    A circular chart divided into sectors, illustrating numerical proportions.

  • Term: Central Angle

    Definition:

    The angle formed at the center of the pie chart corresponding to a particular category.

  • Term: Sector

    Definition:

    A portion of the pie chart that represents a category of data.

  • Term: Percentage

    Definition:

    A fraction of 100, used to express proportions in pie charts.