Pie Chart

A pie chart is a pictorial representation of data in the form of a circular chart or pie where the slices of the pie show the size of the data. A list of numerical variables along with categorical variables is needed to represent data in the form of a pie chart. The arc length of each slice and consequently the area and central angle it forms in a pie chart is proportional to the quantity it represents.

A pie chart is a type of a chart that visually displays data in a circular graph. It is one of the most commonly used graphs to represent data using the attributes of circles, spheres, and angular data to represent real-world information. The shape of a pie chart is circular where the pie represents the whole data and the slice out of the pie represents the parts of the data and records it discretely.

Pie Chart Definition

A pie chart is a type of graph that records data in a circular manner that is further divided into sectors for representing the data of that particular part out of the whole part. Each of these sectors or slices represents the proportionate part of the whole. Pie charts, also commonly known as pie diagrams help in interpreting and representing the data more clearly. It is also used to compare the given data.

Pie Chart Example

Let us look at the following example of the following pie chart that represents the ingredients used to prepare a butter cake.

Example: The whole pie represents a value of 100. It is divided into 10 slices or sectors. The various colors represent the ingredients used to prepare the cake. What would be the exact quantity of each of the ingredients represented in specific colors in the following pie chart?

Solution: As we can see, the pie is divided into 10 slices or sectors. To calculate the exact amount of ingredients that are added to the cake, we divide the whole sector's value, i.e., 100 by the number of sectors. So, 100 ÷ 10 = 10. Hence, looking at the color divisions made in the pie chart we can conclude that:

We know that the total value of the pie is always 100%. It is also known that a circle subtends an angle of 360°. Hence, the total of all the data is equal to 360°. Based on these, there are two main formulas used in pie charts:

• To calculate the percentage of the given data, we use the formula: (Frequency ÷ Total Frequency) × 100
• To convert the data into degrees we use the formula: (Given Data ÷ Total value of Data) × 360°

We can work out the percentage for a given pie chart using the steps given below,

• Categorize the given data and calculate the total
• Divide the different categories
• Convert the data into percentages
• Calculate the degrees

Let us understand the above steps using an example.

Example: Observe the following pie chart that represents the money spent by Ana at the funfair. The indicated color shows the amount spent on each category. The total value of the data is 20 and the amount spent on each category is interpreted as follows:

• Ice Cream - 4
• Toffees - 4
• Popcorn - 2
• Rides - 10

To convert this into pie chart percentage, we apply the formula: (Frequency ÷ Total Frequency) × 100

Let us convert the above data into a percentage:

Amount spent on rides: (10/20)× 100 = 50%

Amount spent on toffees: (4/20)× 100 = 20%

Amount spent on popcorn: (2/20)× 100 = 10%

Amount spent on ice-cream: (4/20)× 100 = 20%

Example:

Observe the following pie chart that recommends a low-carb diet on a day.

We measure the angles of each slice. We get that Protein measures 180°, Carb measures 108°, and Fats measures 72°

To find the percentage, we divide each angle by 360 and multiply it by 100.

Protein = (180/360) × 100 = 50%

Carb = (108/360) × 100 = 30%

Fats = (72/360) × 100 = 20%

Whenever some data has to be represented visually as a fractional part of a whole, we use pie charts. It is used to compare the data and see why one is smaller/greater than the other. Therefore, when we are dealing with a limited number of buckets and discrete data sets, it’s better to use a pie chart. Listed below are a few uses of a pie chart:

• In a business, it is used to compare the growth areas such as profit and loss.
• In school, pie charts are used to show the time allotted to each section, the grades of students in a form of percentages, etc.
• Pie charts are used in comparing the relative size of data of people owning the same vehicles, similar houses, etc.
• They are used to represent the marketing and sales data for the comparison of brands.

We use the following steps to construct a pie chart and using the above-mentioned formulas, we can calculate the data.

• Step 1: Write all the data into a table and add up all the values to get a total.
• Step 2: To find the values in the form of a percentage divide each value by the total and multiply by 100.
• Step 3: To find how many degrees for each pie sector we need, we take a full circle of 360° and use the formula: (Frequency/Total Frequency) × 360°
• Step 4: Once all the degrees for creating a pie chart are calculated, draw a circle (pie chart) using the calculated measurements with the help of a protractor.

Example: Construct a pie chart to visually display the favorite fruits of the students in a class based on the given data: Mango - 45; Orange - 30; Plum - 15; Pineapple - 30; Melon - 30

Solution:

Step 1: Create a table with the values and get the total.

Step 2: Find the percentage of each value:

Mango = (45/150) × 100 = 30%

Orange = (30/150) × 100 = 20%

Plum = (15/150) × 100 = 10%

Pineapple = (30/150) × 100 = 20%

Melon = (30/150) × 100 = 20%

Step 3: Finding the degree of each pie sector using the formula: (Given data/Total Value of data) × 360°

With all the above degrees, with the help of a protractor draw a pie chart. Thus, the pie chart looks like this:

To read or interpret a pie chart, we see if the given chart is given in percentages or without any value. If it is given in percentages, the conversion is made accordingly and interpreted accordingly. Let us look at an example to understand this better.

Example: The pie chart shown below shows the percentages of types of transportation used by 500 students to come to school. With this given information, answer the following questions:
a) How many students come to school by bicycle?
b) How many students do not walk to school?
c) How many students come to school by bus and car?

Solution:

a) The students who come by bicycle = 25%; (25/100) × 500 = 25 × 5 = 125

b) The students who do not walk to school - We need to add the values of all the remaining means, i.e., bus + car + bicycle = 26 + 32 + 25 = 83

Hence, (83/100) × 500 = 83 × 5 = 415 students do not walk to school.

c) The students who come by bus and car [(32 + 26)/100] × 500 = 58 × 5 = 290

Given below are the advantages to a pie chart which are the reasons for the widespread application of pie charts in different fields.

• A pie chart is a simple and easy-to-understand method to represent the data visually as a fractional part of a whole.
• It provides an effective communication tool visually simpler than other types of graphs.
• Pie chart helps in data comparison for the audience at a glance to give an immediate analysis or to quickly understand information due to widespread use in business and the media.

There are few demerits in pie charts. These are as given below,

• A pie chart cannot show more than a few values without separating the visual encoding from the data they represent, that is they are not very effective when the number of values in a data set increases.
• It does not easily reveal exact values in the data set.
• To show the changes in the data, many pie charts may be needed. It, therefore, fails to explain the causes, effects, or patterns.

Related Topics:

Listed below are a few interesting topics that are related to the concept of a pie chart, take a look!

• Measurement
• Angles
• Degrees

What is a Pie Chart?

A pie chart is a circular graph that records data according to numbers, percentages, and degrees. The pie chart is divided into sectors for representing the data of a particular part out of the whole part according to the measurements. Pie charts also called pie diagrams, represent each sector or slice as the proportionate part of the whole. Some of the examples where we use pie charts are in businesses, schools, etc.

What are the Uses of a Pie Chart?

Pie charts are used to represent the proportional data in a single chart. The concept of pie slices is used to show the percentage of a particular data from the whole pie. Pie charts are used in businesses to measure the profit or loss of the company, used in schools to compare the percentages of scores of students, used in marketing and sales materials, and so on.

Should a Pie Chart be equal to 100?

Yes, the total value of the pie chart should be equal to 100. The slices of the pie chart are accordingly expressed as a percentage.

What is the Formula for Pie Chart?

The different formulas that can be used while representing a given data in form of pie charts are as given below,

• To calculate the percentage of the given data we use the formula: (Frequency ÷ Total Frequency) × 100
• To convert the data into degrees we use the formula: (Given Data ÷ Total value of Data) × 360°

How do you Explain a Pie Chart?

To read or explain the information depicted in the form of a pie chart, we see if the given chart is given in percentages or without any value. If it is given in percentages, the conversion is made accordingly and the data can be interpreted accordingly.

How do you Work out Degrees for a Pie Chart?

To convert the data into degrees for a pie chart, we use the formula given below,
(Given Data ÷ Total value of Data) × 360°.

How to Calculate the Percentage of Data in the Pie Chart?

To calculate the percentage of the given data in a pie chart, we can use the formula given below,
(Frequency ÷ Total Frequency) × 100

How to Create a Pie Chart?

We use the following steps to construct a pie chart:

• Step 1: Add all the values to get the total quantity mentioned in the table.
• Step 2: To determine the percentages divide each value by the total and multiply it by 100.
• Step 3: To determine the degrees of each sector, use the formula: (Frequency/Total Frequency) × 360°
• Step 4: Once all the degrees for creating a pie circle are calculated, draw the circle (pie chart) using the calculated measurements with the help of a protractor.

How to Change Pie Chart Numbers to Percentage and Degree?

To calculate the numbers present in the pie chart, we can convert them into percentages and degrees. To convert a value into a pie chart percentage, we use the formula: (Frequency ÷ Total Frequency) × 100. To convert a value into degrees, we use the formula: (Given Data ÷ Total value of Data) × 360°