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 
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.
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:
Example: Let us consider the following example to understand all these steps.
Runs scored by 4 batsmen in a cricket match are:
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:
We can work out the percentage for an assigned pie chart by practicing the steps given below:
Let us understand the abovementioned 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^{∘}
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.
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:
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 T20 Cricket.
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.
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:
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:
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: Number of votes ∝ Angle made in a pie chart
⇒ Angle made by party A/360 = Vote gained by party A/Total votes
⇒ 135/360 = 21960/Total votes
∴ Total votes = 58560.
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 bioreserve 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 sectorCheetah in pie chart 1/360 + 10000 × Angle subtended by sectorCheetah 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
Advantages of Pie Charts
Disadvantages of Pie Charts
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.
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