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Pie Chart

Pie charts are helpful. For instance, businesses can easily display their yearly sales on a pie chart. The pie chart provides a simple picture of how deals were created inside a business. A grocery store, for instance, might use a pie chart to display the number of sales for each item, such as canned goods, dairy items, frozen foods, etc.

Schools can use a pie chart to display the number of students enrolled in each subject in the field of education. Pie charts can also help people better manage their budgets and keep track of where and what they spend their money.

Apart from businesses and schools, pie charts are used in budgeting, financial planning, statistics, research and other fields.

Definition

Pie charts (sometimes called circle graphs) are used to compare data. Slices of different sizes are marked on a circle (i.e. the pie) based on what part of the whole they represent.

What is a Pie Chart?

A pie chart provides a visual picture of how a data set is divided into more manageable chunks using a pie. A pie chart is a graph in circular form divided into different slices where each slice shows the size of the data. 

A single slice of the circle represents each definite value, and the size of each slice reveals how much of the total each category level occupies. In simple terms, every slice represents a fraction of the entire dataset, whereas the whole pie represents the entire dataset. The pie’s pieces are measured as angles out of a possible 360 degrees.

Each slice of the pie chart is also called the sector. For example, the pie chart below shows how much of the total each sector occupies. The percentage of pupils in Mr. Diaz’s class who have favorite TV shows is shown in the pie chart. Anime is a favorite of 35% of the class, Drama is a favorite of 25%, Comedy is a favorite of 15%, Reality is a favorite of 15%, and Documentaries are a favorite of 10%.

Pie charts can be challenging to draw by hand. Thus, it is preferable to create them using software like Excel.

Parts of a Pie Chart

A pie chart has the following parts, the title, the legend, the source and the data/information.

The title tells what is in the pie chart. The title helps the reader understand what they are about to see.

The legend shows the description of each slice in the pie chart. The legend helps the reader comprehend the information that the pie chart offers.

A pie chart’s most essential part is its information or data. Data is displayed in pie charts as a percentage of 100. Each slice represents a distinct piece of data.

The source provides information on where you obtained the data for your graph. The people that gathered your data should be acknowledged.

Types of Pie Charts

Two-dimensional (2D) Pie Chart

The most basic pie chart is the 2D pie chart. The 2D pie chart represents how the data is divided. The pie chart below is an example of a 2D pie chart of the percentage of students enrolled in a school taking up each course.

Three-dimensional (3D) Pie Chart

The pie chart’s visual appeal is frequently enhanced by using the 3D shape. The additional dimension neither hinders the ease of understanding nor adds new information.

Donut Plot

The centre of the pie chart is eliminated in a donut plot. Excess labels can be added to the chart by using the extra space in the centre. The readability of the donut plot and the pie chart is nearly equal. 

Exploded Pie Chart

In an exploded pie chart, a slice or slices are separated from the centre of the pie chart to emphasize a point. The exploding pie chart may make the chart more difficult to read while improving its looks. It is essential only to use the exploded pie chart when necessary.

How to make a Pie Chart

The following are the steps in constructing a pie chart:

Step 1: Arrange the data using a table.
Step 2: Get the sum of all the values.
Step 3: Convert each data into percent to identify which part of the whole it occupies by using the formula: frequency / total frequency x 100.

$\frac{frequency}{total frequency}$ x 100

Step 4: Find each slice/sector’s angle measures using the formula: frequency/ total frequency x 360 degrees.

$\frac{frequency}{total frequency}$ x 360°

Step 5: Draw a circle and use a protractor to make the central angles corresponding to the values of each component.
Step 6: Color-code each slice to denote different components.

Examples

Example 1

The Smith Family has the following weekly expense:

Food ($70), Water ($12), Electricity ($40), Transportation ($20), Medicine ($10), Miscellaneous ($8)

Create a pie chart for the weekly expense of the Smith Family and answer the following questions.

a. Which expense in the Smith Family receives the smallest weekly expense allocation?
b. Which expense in the Smith Family has the largest weekly spending allocation?
c. What percent of total spending goes toward Electricity and Water?

Solution:

Let us follow the steps in constructing a pie chart.

Step 1: Arrange the data using a table.

Arrange the table such that the first column is the expense of the Smith Family, and the second column is the amount spent on each expense.

ExpensesAmount
Food$70
Water$12
Electricity$40
Transportation$20
Medicine$10
Miscellaneous$8

Step 2: Get the sum of all the values.

The total weekly expense of the Smith Family is $160.  (70 + 12 + 40 + 20 + 10 + 8 = 160)

ExpensesAmount
Food$70
Water$12
Electricity$40
Transportation$20
Medicine$10
Miscellaneous$8
Total$160

Step 3: Convert each data into Percent to identify which part of the whole it occupies by using the formula frequency / total frequency x 100.

ExpensesAmountPercent
Food$7043.75 %
Water$127.5 %
Electricity$4025 %
Transportation$2012.5 %
Medicine$106.25 %
Miscellaneous$85 %
Total$160100 %

Food: 70/160 x 100 = 43.75 %

Water: 12/160 x 100 = 7.5 %

Electricity: 40/160 x 100 = 25 %

Transportation: 20/160 x 100 = 12.5 %

Medicine: 10/160 x 100 = 6.25 %

Miscellaneous: 8/160 x 100 = 5 %

Be mindful that the total percentage must be equal to 100 %.

Step 4: Find each slice/sector’s angle measures using the formula frequency/ total frequency x 360 degrees.

ExpensesAmountPercentDegrees
Food$7043.75 %157.5°
Water$127.5 %27°
Electricity$4025 %90°
Transportation$2012.5 %45°
Medicine$106.25 %22.5°
Miscellaneous$85 %18°
Total$160100 %360°

Food: 70/160 x 360° = 157.5°

Water: 12/160 x 360° = 27°

Electricity: 40/160 x 360° = 90°

Transportation: 20/160 x 360° = 45°

Medicine: 10/160 x 360° = 22.5°

Miscellaneous: 8/160 x 360° = 18°

The total sum of all the angles must be equal to 360°.

Step 5: Draw a circle and use a protractor to make the central angles corresponding to the values of each component.

The image below shows the angle measurements of each sector.

Step 6: Color-code each slice to denote different components.

The image below shows the weekly expenses of the Smith Family using a pie chart.

Let us now answer the questions related to this word problem.

a. Which expense in the Smith Family receives the smallest weekly expense allocation
Miscellaneous receives the smallest allocation of 5 % of the total weekly expense.
b. Which expense in the Smith Family has the largest weekly spending allocation?Food receives the largest allocation of 43.75 % of the total weekly expense.
c. What percent of total spending goes toward Electricity and Water?
Electricity and Water receive 25% and 7.5% of the weekly expense, respectively. If we get the total of these, we have 25 % + 7.5 % =32.5 %. Thus, the Smith Family allocates 32.5% of their total expense to electricity and water.

Example 2

The data below shows the number of different fruits harvested on a farm. Represent the data using a pie chart and answer the questions below.

ApplesMangoesOrangesJackfruitsPearsWatermelons
8010085354555
  1. Find the sum of the harvested fruits on the farm?
  2. What percent of the total harvest is the mangoes?
  3. What percent of the total harvest is the oranges?
  4. What fraction of the total harvest represents the apples?
  5. What fraction of the total harvest represents the watermelons?
  6. What percent of the harvest is jackfruits and pears?

Solution:

Let us follow the steps in constructing a pie chart.

Step 1: Arrange the data using a table.

Organize the table so that the type of fruit harvested is in the first column and the number of fruits is in the second.

Type of FruitsQuantity
Apples80
Mangoes100
Oranges85
Jackfruits35
Pears45
Watermelons55

Step 2: Get the sum of all the values.

The total fruits harvested on the farm were 400.  (80 + 100 + 85 + 35 + 45 + 55 = 400)

Type of FruitsQuantity
Apples80
Mangoes100
Oranges85
Jackfruits35
Pears45
Watermelons55
Total400

Step 3: Convert each data into Percent to identify which part of the whole it occupies by using the formula frequency / total frequency x 100.

Type of FruitsQuantityPercent
Apples8020 %
Mangoes10025 %
Oranges8521.25 %
Jackfruits358.75 %
Pears4511.25 %
Watermelons5513.75 %
Total400100 %

Apples: 80/400 x 100 = 20 %

Mangoes: 100/400 x 100 = 25 %

Oranges: 85/400 x 100 = 21.25 %

Jackfruits: 35/400 x 100 = 8.75 %

Pears: 45/400 x 100 = 11.25 %

Watermelons: 55/400 x 100 = 13.75 %

Keep in mind that the percent must add up to 100 percent.

Step 4: Find each slice/sector’s angle measures using the formula frequency/ total frequency x 360 degrees.

Type of FruitsQuantityPercentDegrees
Apples8020 %72°
Mangoes10025 %90°
Oranges8521.25 %76.5°
Jackfruits358.75 %31.5°
Pears4511.25 %40.5°
Watermelons5513.75 %49.5°
Total400100 %360°

 Apples: 80/400 x 360 =72°

Mangoes: 100/400 x 360 = 90°

Oranges: 85/400 x 360 = 76.5°

Jackfruits: 35/400 x 360 = 31.5°

Pears: 45/400 x 360 = 40.5°

Watermelons: 55/400 x 360 = 49.5°

360 degrees must be the result of adding up all the angles.

Step 5: Draw a circle and use a protractor to make the central angles corresponding to the values of each component.

The image below shows the angle measurements of each sector.

Step 6: Color-code each slice to denote different components.

Let us now answer these questions:

  1. Find the sum of the harvested fruits on the farm?

A total of 400 fruits were harvested on the farm.

  1. What percent of the total harvest is the mangoes?

25% of the harvested fruits are mangoes.

  1. What percent of the total harvest is the oranges?

21.25% of the harvested fruits are oranges.

  1. What fraction of the total harvest represents the apples?

To find the fraction of the total harvest that represents apples, we have 80/400.

Simplifying 80/400, we must divide the numerator and the denominator by their greatest common factor, which is 80.

$\frac{80÷80}{400÷80}=\frac{1}{5}$

Thus, 1/5 is the fraction of the total harvest that represents apples.

  1. What fraction of the total harvest represents the watermelon?

We have 55/400 to find the fraction of the total harvest that represents watermelons. 

Simplifying 55/400, we must divide the numerator and the denominator by their greatest common factor, which is 5.

$\frac{55÷5}{400÷5}=\frac{11}{80}$

Therefore, 11/80 is the fraction of the total harvest that represents watermelons.

  1. What percent of the total harvest is jackfruits and pears?

Since 8.75% represents the jackfruits and 11.25 % represents the pears, the, adding these percentages together we have, 8.75 % + 11.25 % = 20 %. 

Hence, 20% of the total harvest on the farm is jackfruits and pears.

Example 3:

Complete the table below and create a pie chart that shows the favorite subject of 50 students. 

SubjectsNumber of StudentsPercentDegrees
English1326 %
Mathematics918 %
Science1224 %
History612 %
Physical Education1020 %
Total

Solution:

Percent Computation

English: 13/50 x 100 = 26 %

Math: 9/50 x 100 = 18 %

Science: 12/50 x 100 = 24 %

History: 6/50 x 100 = 12 %

Physical Education: 10/50 x 100 = 20 %

Degrees Computation

English: 13/50 x 360° = 93.6°

Math: 9/50 x 360°  = 64.8°

Science: 12/50 x 360° = 86.4°

History: 6/50 x 360° =43.2° 

Physical Education: 10/50 x 360° = 72°

Therefore, the table below shows the complete data followed by the pie chart that represent the favorite subjects of 50 students.

SubjectsNumber of StudentsPercentDegrees
English1326 %93.6°
Mathematics918 %64.8°
Science1224 %86.4°
History612 %43.2°
Physical Education1020 %72°
Total50100 %360°

Example 4:

Complete the table below about the different flowers a florist has. Create a pie chart and answer the following questions:

  1. What is the total number of flowers?
  2. What percent of the flowers are Lilies?
  3. What percent of the flowers are Daisies?
  4. How many percent of the total flowers are Sunflowers and Carnations?
  5. What fraction of the total flowers represent Roses?
SubjectsNumber of StudentsPercentDegrees
Roses4026 %
Lilies5018 %
Sunflowers7024 %
Carnations10512 %
Chrysanthemums8520 %
Daisies150
Total

Solution:

Percent Computation

Roses: 40/500 x 100 = 8 %

Lilies: 50/500 x 100 = 10 %

Sunflowers: 70/500 x 100 = 14 %

Carnations: 105/500 x 100 = 21 %

Chrysanthemums: 85/500 x 100 = 17 %

Daisies: 150/500 x 100 = 30 %

Degrees Computation

Roses: 40/500 x 360°= 28.8°

Lilies: 50/500 x 360° = 36°

Sunflowers: 70/500 x 360° = 50.4°

Carnations: 105/500 x 360° = 75.6°

Chrysanthemums: 85/500 x 360° = 61.2°

Daisies: 150/500 x 360° = 108°

Hence, the table below shows the complete data followed by the pie chart that represents the number of the different types of flowers of the florist.

SubjectsNumber of StudentsPercentDegrees
Roses408 %28..8°
Lilies5010 %36°
Sunflowers7014 %50.4°
Carnations10521 %75.6°
Chrysanthemums8517 %61.2°
Daisies15030 %108°
Total500100 %360°

Here are the answers to the questions:

  1. What is the total number of flowers the florist has?
    The florist has a total of 500 flowers.
  2. What percent of the flowers are Lilies?
    10% of the total flowers are Lilies.
  3. What percent of the flowers are Daisies?
    30% of the total flowers are Daisies.
  4. How many percent of the total flowers are Sunflowers and Carnations?
    Since the percentage of Sunflowers is 14 % and the Carnations is 21%, the total percentage of Sunflower and Carnations altogether is 35 %.
  5. What fraction of the total flowers represent Roses?
    The fraction of the total flowers that represent Roses is 40/500. This fraction can still be simplified by dividing the numerator and the denominator by 20.

$\frac{40÷20}{500÷20}=\frac{2}{25}$.

Hence, 2/25 is the fraction of the total flowers that represents the Roses. 

Pie Charts: Key Points to Keep in Mind

Keep an Eye on the Centre

When creating a pie chart, make sure to set the centre correctly so that the angles of each sector are labelled appropriately.

Use Clear Colors

In a pie chart, colors are significant. It is crucial to choose colors that set one sector apart from another. If the colors are the same shade or not different from one another, the readers could become confused.

Think About the Pattern of Slices

A reader can understand the pie chart much more quickly if the slices are presented in proper order. When there are categories with values that are pretty comparable, a standard ordering that goes from the largest piece to the smallest slice is highly helpful. 

Use Fewer Slices and Colors in the Chart

Pie charts with several slices might be challenging to read. Small pieces may be difficult to see, and you must use different colors to make them distinct. There are varying opinions on this, but make sure that the number of slices and colors you use help the reader to understand the chart quickly.

Use Distortions Carefully

This typically applies to 3D pie charts since the gaps can make it more challenging to assess the part-to-whole comparison. Some distortions create unnecessary effects on the chart, so it should be made carefully. Distortions may cause the reader to compare the pieces and notice that one seems larger than the other, which is inconsistent with the number. 

Avoid Representing Conflicting Data

If the data in a pie chart is fragmented and not all of the data in the set, then the pie chart is meaningless. Make sure there is consistency in the pie chart presented and all data are present.

Summary

  • A pie chart provides a visual picture of how a data set is divided into more manageable chunks using a pie. A pie chart is a graph in circular form divided into different slices where each slice shows the size of the data. 
  • Each slice of the pie chart is also called the sector.
  • The common parts of a pie chart are the title, the legend, the data, and the source.
  • The different types of pie charts are the Two-dimensional (2D) Pie Chart, Three-dimensional (3D) Pie Chart, Donut Plot, and Exploded Pie Chart.
  • These are the steps in constructing a pie chart:

Step 1: Arrange the data using a table.
Step 2: Get the sum of all the values.
Step 3: Convert each data into Percent to identify which part of the whole it occupies by using the formula: frequency/total frequency x 100.

$\frac{frequency}{total frequency}$ x 100

Step 4: Find each slice/sector’s angle measures using the formula: frequency/ total frequency x 360 degrees.

$\frac{frequency}{total frequency}$ x 360°

Step 5: Draw a circle and use a protractor to make the central angles corresponding to the values of each component.
Step 6: Color-code each slice to denote different components.

Pie Graph (International Women’s Day Themed) Math Worksheets
Hundreds Charts (Fashion Themed) Worksheets
Line Graphs (International Nurses Day Themed) Math Worksheets

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