Overview: Pie Chart

# Overview: Pie Chart | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

 Table of contents What is Pie Chart? How to Create a Pie Chart Pie Chart Formula Types of Pie Charts Solved Examples of Pie Chart

## What is Pie Chart?

Pie chart is a circular graph that is divided into slices and each slice represents a numerical proportion that is proportional to the quantity of the item it represents. A Pie Chart (Pie Diagram) is a graphical representation of statistical data in the form of a circular graph. The division of the slices is also based on their quantity which means that the angle and the arc length of each slice are proportional to the quantity that the particular slice represents.

## How to Create a Pie Chart

To create a pie chart, you must know the numerical distribution of the categories to be included in the pie chart. Once you have all the categories and their corresponding data, then follow the given steps to create a pie chart. All the slices of the pie chart make up 360 degrees and all the data when combined make up 100 percent.

We can create a pie chart by following the below steps:

• Step 1: Distribute the data according to their categories.
• Step 2: Calculate the total.
• Step 3: Convert the data into percentages by dividing the numerical value of each category with the total calculated in Step 2 and multiplying by 100.
• Step 4: Calculate the degrees of each category by dividing the numerical value of each category with the total calculated in Step 2 and multiplying by 360.
• Step 5: Draw a circle and using a protractor, draw the pie chart according to the degrees calculated for each category in Step 4.

Example: Let us consider the following example to understand all these steps.
Runs scored by 4 batsmen in a cricket match are:

• Step 1: is done with this table.
• Step 2: Calculating the total 24+36+12+38=110
• Step 3: Calculating individual percentages.
• Step 4: Calculating individual degrees.
• Step 5: According to the degrees calculated, draw a pie diagram using a protractor and mention the percentage of runs scored by each player along with their name.

## Pie Chart Formula

We remember that the complete value of the pie is always 100%. It is also recognized that a circle subtends an angle of 360°. Therefore, the sum of all the data is equivalent to 360°. Depending on these, there are two principal formulas applied in pie charts:

• To determine the percentage of the provided data, the formula we practice is (Frequency ÷ Total Frequency) × 100
• To switch the data into degrees the formula we will be using is (Given Data ÷ Total value of Data) × 360°

We can work out the percentage for an assigned pie chart by practicing the steps given below:

• Classify the presented data and estimate the total.
• Arrange the various categories.
• Switch the data into percentages.
• Compute the degree values.

Let us understand the above-mentioned steps of pie chart with the help of an example.

Example: Following pie chart shows the percentage of Testbook users from different states of India.

Total number of users = 15 lakhs

Find the central angle made by Bihar in the pie chart.

Solution: Number of users in Bihar = 15,00,000 × 30% = 4,50,000
Total users = 15,00,000
15,00,000 users = 360

## Types of Pie Charts

There are several ways in which a pie chart can be drawn, according to the demands. Following are a few types of the most commonly used pie charts.

### 2D Pie Chart with Percentage

While comparing data, when you wish to know the exact percentage of distribution of the quantity, then you make use of these types of pie diagrams. These are useful when you need to make calculations based on the distribution of data represented by the pie diagrams.
In this type of pie diagram, the data is represented through a circle, with sections at particular angles (proportional to the data they represent). The quantity that a particular section/slice represents and the percentage of that quantity are marked by an arrow. See the following example to understand:

### 2D Pie Chart without Percentage

When you only want to compare data, and you are not interested in the numerical proportions of the quantities in that data set, then you can make use of this type of pie diagram. They are useful when you only want to know which quantity is more or less compared to others, and you do not need to perform any calculations. For example, if you want to know which country has the maximum population of Vegans in the world, and what are the other succeeding countries, then you make use of such types of pie diagrams. Here you are not interested in the percentage of the vegan population, but only interested in the comparison.

In this type of pie diagram, the distribution is distinguished by the different colors of the slices. The item represented by each color is written beside the pie chart. Consider the following example shows the points scored by the 8 teams in T-20 Cricket.

### Doughnut Pie Chart

This pie diagram is in the shape of a doughnut with a hollow circle in the center of the pie diagram. The hollow center is used to represent the information that is applicable to all the other slices of the pie diagram. A doughnut pie diagram can be used to represent multiple statistics at the same time. Hence, it is usually better than the normal pie chart as the ratio of data intensity is better. In the following example of a doughnut pie diagram, the points scored in a game by four teams are represented.

### Exploded Pie Chart

In this type of Pie diagram, one or more sections/slices of the pie chart are separated from the rest of the chart. These types of pie charts are useful when you need to highlight a particular section of the pie chart. For example:

### 3D Pie Chart

All of the above types of pie diagrams were 2D, and all of them can be represented in the 3D format as well. There is no particular difference except for the visual effects. A 3D pie diagram looks visually more appealing than a 2D pie diagram. For example:

### Interpreting Pie Chart

For the interpretation of a pie chart, the first thing to notice is what is the format of the given chart. That is if the given data is in percentages or without percentages. Depending on the given data conversion is made accordingly. Let us understand two examples to understand the above concepts.

Example 1: The election result in which six parties contested was depicted by a pie chart. Party A had an angle 135∘ on this pie chart. If it secured 21960 votes, how many valid votes in total were cast?
Sol:
⇒ Angle made by party A/360 = Vote gained by party A/Total votes

Example 2: Study the following pie chart and answer the following question based on them. The pie chart represents the number of animals of each species (as the angle subtended) in a bio-reserve for two years.

The total populations of animals in the year 2018 and 2019 are 5000 and 10000 respectively. A pie chart was made with the average populations of the animals in the year 2018 and 2019. What will be the angle subtended by the sector representing the cheetah in the pie chart (in degrees)?
Sol:
Average total population = (5000 + 10000)/2 = 7500
The average population of cheetah = {(5000 × Angle subtended by sector-Cheetah in pie chart 1/360 + 10000 × Angle subtended by sector-Cheetah in pie chart 2/360)}/2
={ (5000 × 64.8/360 + 10000 × 81/360)}/2 = (900 + 2250)/2 = 1575
Angle subtended by sector representing cheetah in average pie chart = 1575/7500 × 360 = 75.6.

Uses of Pie Charts

• Pie charts find considerable use in business and the mass media world. In the business world, people usually make use of pie charts in their presentations to represent the percent of profit, loss, growth, turnover, etc.
• Other industries as well, use pie charts to statistically represent the data regarding their customers, retail, investment, return on investment, and other such parameters.
• Some might use pie charts to represent the data of different products of the same industry.

• Visual representation makes it easier and quicker for the readers to analyze the distribution of data.
• It is useful during presentations when you need to understand the data at a glance.
• When comparing data of different categories, it is better to use pie charts as you can quickly compare the data because of the visual representation without going into many statistical details.

• It is difficult to compare many quantities using pie charts, as the chart may become crowded and visually difficult to interpret.
• You can only compare quantities that fall under a single data set. If you have to compare multiple sets of data with many quantities, then you will need multiple pie charts.
• It is difficult to compare different slices of the same pie chart and also difficult to compare different pie charts.

## Solved Examples of Pie Chart

Given below are a few solved examples of Data Analysis and Data Interpretation using pie charts.

Example. The following chart represents monthly expenses of Anil.

(i) If Anil spends Rs. 6000 more on food and shopping together than he spends on rent, then find his monthly expenses in Rs.
Sol:
Monthly expenses = 100% [Total of a pie chart is always 100%]
∴ Expenditure on food and shopping together = 22%+8% = 30%
∴ Expenditure on rent = 15%
According to the question,
⇒ 30%-15%=Rs.6000
⇒ 15%=6000
⇒ 100%=6000 * 100/15
Now, According to the unitary method,
⇒ 100*1/100=6000 * 100/15

⇒ 400*100
⇒ Rs.40,000.
Hence, monthly expenses of Anil are Rs. 40,000.

(ii) Anil spends 20% of his expenditure on other on transportation, which amounts to Rs.2,100. Then find his expenditure on education.
Sol: Expenditure on transportation =20% of 35%
⇒ 7% = 2100
⇒ 1% = 300
Expenditure on education =20%
⇒ Total monthly expenses = Rs.40,000 [From question 1]
⇒ 20% of 40,000 = Rs. 8000
Hence, the expenditure on education is Rs. 8,000.

The document Overview: Pie Chart | Logical Reasoning (LR) and Data Interpretation (DI) - CAT is a part of the CAT Course Logical Reasoning (LR) and Data Interpretation (DI).
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## Logical Reasoning (LR) and Data Interpretation (DI)

131 videos|171 docs|117 tests

## Logical Reasoning (LR) and Data Interpretation (DI)

131 videos|171 docs|117 tests

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