## What is a Pie Chart?

A pie chart is a statistical, circular illustration. It is divided into segments to denote numerical proportions of different quantities. It shows the distribution of data that has a discrete set.

Each segment, or slice, of a pie chart, represents a certain proportion of a total quantity. The value of each slice is denoted in either percentage or in the form of an angle.

Since the pie chart is circular, the total angle that corresponds to the entire data set is 360 degrees, which is equal to one entire circular rotation.

In this guide, we shall teach you how to measure the angle of a pie chart segment from given data sets or percentages to find out the real, numerical value of the quantity. So let’s get started!

## Measuring the Angle of a Pie Chart: A Step-By-Step Guide

In this section, you will learn how to measure the angle of a pie chart through two worked examples.

### Worked Example # 1 – Beverages:

Let’s suppose there are 150 students in a university class. They were all surveyed and asked about their favorite beverage (non-alcoholic) that they like to drink on a regular basis. The following are the responses that were received:

**Beverages**

**Percentage of Respondents**

Coffee

30%

Tea

20%

Soda

30%

Water

10%

Others

10%

Now, if I ask you how many students prefer tea, you would do the following calculation and tell me your answer:

**Number of students who prefer tea** = 20% × 150 students

= 20/100 x 150

= 30 students

Similarly, for each beverage, you can do the calculation similar to the one given above and get your answer.

If you are then asked to construct a pie chart depicting the information you have collected about students and beverages, here is what you should do:

*Step 1 – Calculate the Exact Number of Students Who Prefer Each Beverage:*

**Coffee:**

30/100 × 150 = 45 students

**Tea:**

20/100 × 150 = 30 students

**Soda:**

30/100 × 150 = 45 students

**Water:**

10/100 × 150 = 15 students

**Others:**

10/100 × 150 = 15 students

*Step 2 – Calculate the Angle of Each Segment/Slice of the Pie Chart Using a Formula:*

**Angle of slice = frequency of data/total frequency × 360 degrees**

Let's use this formula in our example of beverages. We know that 45 students like coffee, so the angle of the segment of the pie chart that denotes coffee consumers will be:

Angle of coffee segment = people who prefer coffee/total students surveyed × 360 degrees

= 45/150 × 360°

= 108 degrees

In the same way, you can now calculate the angles in degrees for every beverage before you proceed to construct the pie chart:

**Coffee:**

45/150 × 360° = 108°

**Tea:**

30/150 × 360° = 72°

**Soda:**

45/150 × 360° = 108°

**Water:**

15/150 × 360° = 36°

**Others:**

15/150 × 360° = 36°

*Step 3 – Draw the Pie Chart Using the Angles:*

Once you have all the angles, you can then draw a pie chart. Make sure to label all the segments with the names of the beverages and write percentages or angles in degrees inside the slices. That’s it! Your pie chart is ready.

### Worked Example # 2 – Transportation:

Let’s suppose that you conducted a survey of 100 people for a school project and asked them their preferred mode of transportation. You gave them 5 choices: car, bus, taxi, subway and others. You presented your results in a pie chart to your friend as shown below:

**KEY**

Car

Bus

Taxi

Subway

Others

Your friend has no other information but this pie chart and he has to present the data in a tabular form with discrete numerical values to your teacher. Let’s look at the steps he should take:

*Step 1 – Measure the Angle of the Pie Chart:*

Measure the angle of every segment in the pie chart. Keep the straight 0° line marked on the protractor on one of the straight sides of a segment and read the degrees marked on the protractor on the other straight side of the segment. The answer is the angle of the segment or the slice. Repeat this step for every segment of the pie chart until you have an answer in degrees for each mode of transportation.

*Step 2 – Calculating the Frequency of Data:*

Using the formula given below, calculate the frequency in discrete values:

**Frequency of data = (angle of sector ÷ 360 degrees) × total frequency**

Use this formula for every mode of transportation to get the number of people who preferred it. Let’s suppose your friend calculated the segment of Subway to be 90 degrees:

No. of people who preferred riding the bus = (angle ÷ 360°) × total people surveyed

= (90° ÷ 360°) × 100

= 25 people preferred riding the Subway

*Step 3 – Construct a Table Using the Data:*

Once your friend has the exact numbers of people who preferred a particular mode of transportation, he can then present the results to your teacher in the following tabular form:

**Mode of Transportation**

**No. of people who preferred**

Car

xx

Bus

xx

Taxi

xx

Subway

25

Others

xx

**TOTAL**

**100**

# You’re Ready Now!

We hoped you liked our detailed guide on how to construct and measure the angle of a pie chart. Visit our website for more such lectures and become a pro at statistical illustrations today!