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RS Aggarwal Solutions Class 8 Chapter-24 Pie Charts (Ex 24A) Exercise 24.1

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RS Aggarwal Solutions Class 8 Chapter-24 Pie Charts (Ex 24A) Exercise 24.1 - Free PDF

Free PDF download of RS Aggarwal Solutions Class 8 Chapter-24 Pie Charts (Ex 24A) Exercise 24.1 solved by Expert Mathematics Teachers on Vedantu.com. All Exercise 24.1 Questions with Solutions for Class 8 Maths  RS Aggarwal to help you to revise the complete syllabus and score more marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance Exams.

Pie Chart

A Pie Chart is a type of graph that displays data in a circular graph. The slices of the pie represent the relative size of the data and are a type of pictorial data representation. A Pie Chart necessitates a list of categorical and numerical variables. In this case, the term "pie" refers to the whole, and the "slices" refer to the parts of the whole.

What exactly is a Pie Chart?

The "Pie Chart" is also referred to as a "Circle Chart" because it divides the circular statistical graphic into sectors or sections to illustrate numerical problems. Each sector represents a proportionate portion of the total. The Pie-Chart is the best tool for determining the composition of something at that time. In most cases, Pie Charts take the place of other graphs such as bar graphs, line plots, histograms, and so on.

Formula

The Pie Chart is a popular method of data representation. It has various segments and sectors, and each segment and sector of a Pie Chart represents a specific portion of the total (percentage). The total of all the data is 360°. The total value of the pie is always one hundred percent.

Follow the Steps Below To Calculate the Percentage for a Pie Chart:

  • Sort the information into categories.

  • Determine the total.

  • Separate the categories.

  • Convert to a percentage.

  • Finally, total the degrees.

Maker of Pie Charts

You have now learned how to use geometric tools to create a Pie Chart for the given data. This section will teach you how to create a Pie Chart using an online tool. To create the desired Pie Chart, people frequently use the graphing feature in Excel sheets. We have, however, provided an online Pie Chart maker.

Pie Charts have a fairly narrow use case that is particularly well encapsulated by their definition. To use a Pie Chart, you must have a whole amount that has been divided into a number of distinct parts. In a Pie Chart, your primary goal should be to compare each group's contribution to the whole, rather than comparing groups to each other. If the above criteria are not met, the Pie Chart is inapplicable, and a different plot type should be used instead.

The values that make up a whole and the categories that divide the whole are generally of two types. First and foremost, when the 'whole' represents a total number. Examples include the number of votes cast in an election divided by candidate, or the number of transactions divided by user type (e.g. guest, new user, existing user).

When the total is a sum over an actual data variable, this is referred to as the second type of 'whole.' For Example, we might be interested in the monetary total of all transactions rather than the number of transactions. Dividing this total by an attribute such as user type, age bracket, or location may reveal where the business is most successful.

A Pie Chart's data can be summarised in a table like the one above, where the first column represents a category and the second column represents the proportion, frequency, or amount of that category. Unless it is to be listed somewhere else on a generated figure, the total usually does not need to be specified separately. Alternatively, some tools can simply work with the unaggregated data as shown in the table below, aggregating it into the table above at the time of Pie Chart creation.

How Do You Answer Pie Chart Questions?

This section will teach you how to solve or interpret the Pie Chart to obtain the original values. To do so, we must first determine whether the given chart is presented in percentages, degrees, or without a value. We can answer the questions about Pie Charts using this information. Let's take a look at the solved Example to get a better understanding of this.

Pie Chart Applications

  • It is used in business to compare areas of growth such as turnover, profit, and exposure.

  • To display categorical data.

  • To demonstrate a student's performance in a test, etc.

Advantages

  • The illustration is straightforward and simple.

  • Data can be visually represented as a fraction of a whole.

  • It contributes to the provision of an effective communication tool for even the most uninformed audience.

  • At a glance, provides a data comparison for the audience to provide an immediate analysis or to quickly understand information.

  • There is no need for readers to Examine or measure underlying numbers, which can be avoided by using this chart.

  • You can manipulate data points in the Pie Chart to emphasize a few points you want to make.

Disadvantages

  • It becomes less effective when there are too many data points to use.

  • If there are too many data points. Even if you include data labels and numbers, they may become crowded and difficult to read.

  • Because this chart only represents one data set, a series is required to compare multiple sets.

  • This may make it more difficult for readers to quickly analyze and assimilate information.

Producing a Pie Chart

The following steps are used to create a Pie Chart, and the data is calculated using the above-mentioned formulas.

Step 1: Enter all of the data into a table and total all of the values.

Step 2: To find the percentage values, divide each value by the total and multiply by 100.

Step 3: To calculate the number of degrees required for each pie sector, we take a full circle of 360° and apply the formula: 360° (Frequency/Total Frequency)

Step 4: Once all of the degrees for making a Pie Chart have been calculated, use a protractor to draw a circle (Pie Chart) using the calculated measurements.

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FAQs on RS Aggarwal Solutions Class 8 Chapter-24 Pie Charts (Ex 24A) Exercise 24.1

1. What is a pie chart as defined in the Class 8 Maths syllabus?

A pie chart is a circular statistical graphic used in data handling to show the relationship between a whole and its parts. The entire circle represents the total value (or 100%), while the different slices, known as sectors, represent the proportionate value of each individual component. It is a visual tool for comparing the contribution of each category to the whole.

2. How do the solved problems in RS Aggarwal Solutions for Chapter 24 help master pie charts?

The RS Aggarwal Solutions for Chapter 24 provide detailed, step-by-step methods that are crucial for mastering pie charts. They help by:

  • Illustrating the correct way to calculate the central angle for each data component, a fundamental step in construction.

  • Demonstrating how to interpret existing pie charts to find actual values or percentages.

  • Building problem-solving speed and accuracy, which is essential for Class 8 exams, by providing clear worked-out examples for every question in Exercise 24.1.

3. What are the step-by-step instructions for constructing a pie chart for a given dataset?

To construct a pie chart accurately, as shown in the solutions for RS Aggarwal Class 8, follow these essential steps:

  • Step 1: Sum all the individual data values to find the total frequency.

  • Step 2: Calculate the central angle for each data component using the formula: Central Angle = (Value of Component / Total Value) × 360°.

  • Step 3: Use a compass to draw a circle of a suitable size.

  • Step 4: Draw one radius to act as a baseline. Use a protractor to measure and draw the first sector based on its calculated central angle.

  • Step 5: Using the new line as a baseline, continue to draw the other sectors consecutively until the circle is complete. Be sure to label each sector clearly.

4. Why is it essential to calculate the central angle for each sector in a pie chart?

Calculating the central angle is the most critical step because it ensures that the size of each sector is mathematically proportional to the quantity it represents. The entire circle is 360°, which corresponds to the total sum of the data. By converting each component's fraction of the whole into a corresponding angle, you create a visually accurate representation. An incorrect angle would distort the chart and lead to false conclusions about the data's distribution.

5. How do you find the actual value represented by a sector in a pie chart if the total value is known?

To determine the actual value of a specific component from its sector in a pie chart, you use its central angle. The formula is: Value of Component = (Central Angle of the Sector / 360°) × Total Value. This calculation effectively reverses the process of creating a pie chart and is a common type of problem found in Chapter 24, Exercise 24.1.

6. When would it be more appropriate to use a bar graph instead of a pie chart?

A bar graph is more appropriate than a pie chart when the goal is to compare individual data categories with each other, rather than showing their proportion to a whole. A bar graph is also a better choice in the following situations:

  • When comparing data over a period of time.

  • When there are many categories, which would make a pie chart cluttered and difficult to read.

  • When the sum of the components does not equal a meaningful whole.

7. What is a common mistake students make while solving problems on pie charts?

A frequent mistake is confusing a component's percentage with its central angle. For example, a student might incorrectly draw a 20% sector as a 20° angle. The correct method is to first convert the percentage to an angle by calculating (20 / 100) × 360° = 72°. Always ensure you convert fractions or percentages into degrees before using a protractor to draw the sectors.