What is a pie chart?

A circular graph that shows data in the form of a circle is known as a pie chart

 

Just like the slices of a pizza in which each slice represents the relative size of the whole pizza, each slice in a pie chart depicts the relative size of the data. The term "pie" depicts the whole and the "slices" show parts or elements of the whole. We can also say that a pie chart is a pictorial representation of the data. To make a pie chart, you will need a list of categorical and numerical variables.

Because the pie chart is circular, so it is also known as a circle chart. It breaks down the statistical graphic into slices or sectors. Pie charts work best when we have to show a composition of the whole. 

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Formula

Pie chart has a great importance in statistics. Its slices are also known as sectors which represent the degree of the whole. The degree of the entire pie-chart is equal to 360^o. The formula for pie chart is given below:

= \frac {Given \hspace{0.5cm} data} {Total \hspace{0.5cm} value \hspace{0.5cm} of \hspace {0.5cm} data} \times 360^o

Finding Percentage From a Pie Chart

The total value of the pie chart in percentage is always 100%. Follow these steps to find the percentage of a sector or slice from a pie chart:

  • Step 1 : Classify the data
  • Step 2 : Compute the total
  • Step 3 : Break down the categories
  • Step 4: Convert categories into percentages
  • Step 5: Compute the degrees

Advantages of Using a Pie-chart

Some of the advantages of using a pie chart are given below:

  • This pictorial graph helps to understand the data easily
  • It gives a visual representation of the data as a fractional part of the whole
  • For a layman, this tool is effective because it can be easily understood unlike other graphs
  • It gives an immediate data comparison

Disadvantages of Using a Pie chart

Some of the disadvantages of using a pie chart are given below:

  • If there is a lot of data, then it becomes ineffective
  • If too much data is represented by a pie chart, then it becomes visually impossible for a reader to comprehend it.

In the next step, we will solve some examples in which we will make pie charts from the given data set and find the unknown values from the given pie charts.

Example 1

A survey was conducted in a class to determine the favorite subject of students. The results of the survey are given below:

15 students like mathematics

20 like science

10 like computer science

25 like physics

15 like history

Make a pie chart using the above data.

Solution

Follow these steps to make a pie chart:

Step 1

Make a table of the data like this:

SubjectNumber of Students
Mathematics15
Science20
Computer science10
Physics25
History15

Step 2

Take an aggregate of all the values. The sum of all the values in this example is 85.

Step 3

Calculate the percentage of each subject by dividing each number by total and multiplying it by 100%.

Mathematics = \frac {15}{85} \times 100% = 17.6%

Science = \frac {20}{85} \times 100% = 23.5%

Computer science = \frac {10}{85} \times 100% = 11.8%

Physics = \frac {25}{85} \times 100% = 29.4%

History = \frac {15}{85} \times 100% = 17.6%

Step 4

Divide each value by total and multiply it with 360^o to get the degree:

Mathematics = \frac {15}{85} \times 360^o = 63.5^o

Science= \frac {20}{85} \times 360^o = 85^o

Computer science = \frac {10}{85} \times 360^o = 42. 2^o

Physics = \frac {25}{85} \times 360^o = 105.8^o

History = \frac {15}{85} \times 360^o = 63.5^o

Step 5

Now, draw a circle using a compass and use a protector to measure the degree of each sector. The pie chart of this example is shown below:

 

Example 2

A group of people was asked about the kind of activity they do daily to remain fit. Based on their responses, the following pie chart was developed.

a) What percentage of people said that they do running to keep themselves fit?

b) If a total of 217 people were interviewed, then how many people said that they walk daily to remain fit?

c) What part of the angle of the sector represented by the gym?

Solution

We will find solutions to each part like this.

Part a

Percentage of people who run daily to remain fit = ?

Total percentage of other activities = 15% + 29% + 11% + 26% = 81%

Percentage of people who run daily to remain fit = 100% = 81% = 19%

Hence, 19% of the total people run daily to keep themselves fit.

 

Part b

Percentage of people who walk daily to remain fit = 26%

Total number of people = 217

Number of people who walk daily to remain fit = \frac {26}{100} \times 217 = 56

Hence, 56 people said that they walk daily to remain fit.

 

Part c

Percentage of people who go to gym = 11%

Total number of people = 217

Number of people who go to gym daily = \frac {11}{100} \times 217 = 24

Angle of sector represented by the gym = \frac {24}{217} \times 360^o \approx 40^o

Hence, the angle of the sector represented by the gym is 40^o.

 

Example 3

The monthly salary of John is $4000. He spends $1200 on rent, $400 on utility bills, $300 on transport, $800 on shopping, $450 on groceries and save the remaining money. Find the central angle of the pie chart representing each of these categories.

Solution

Total salary = $4000

Amount spent on rent = $1200

Central angle of the pie chart represented by rent = \frac {1200}{4000} \times 360^0 = 108^o

Central angle of the pie chart represented by utility bills = \frac {400}{4000} \times 360^0 = 36^o

Central angle of the pie chart represented by transport = \frac {300}{4000} \times 360^0 = 27^o

Central angle of the pie chart represented by shopping = \frac {800}{4000} \times 360^0 = 72^o

Central angle of the pie chart represented by groceries = \frac {450}{4000} \times 360^0 = 40.5^o

Central angle of the pie chart represented by savings = \frac {850}{4000} \times 360^0 = 76.5^o

 

Example 4

If 55% of the students in the college who graduated this year got jobs in the first month after graduation, then what is the central angle of the pie chart representing the graduates who got the job within the first month of graduation?

Solution

Percentage of students who got the job within the first month = 55%

Central angle of the pie chart representing these graduates = \frac {55}{100} \times 360^o = 198^o

 

Example 5

150 students were interviewed in a school about their favorite profession. The central angle of the sector representing medical as a preferred profession is 32^o. How many students said that medical is their favorite/preferred profession?

Solution

Total number of students interviewed = 150

The central angle of the pie chart represented by medical = 32^o

First, we will convert the angle into percentage and then use the percentage to compute the number of students opting for a medical profession.

Percentage of students who preferred medical = \frac {32}{360} \times 100% = 8.8%

Number of students who said medical is their preferred profession = \frac {8.8}{100} \times 150 = 13

Hence, out of 150 students, 13 students said that their favorite profession is medical.

 

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.