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.
|1.||What are Pie Charts?|
|2.||Uses of Pie Charts|
|3.||Pie Charts Formula|
|4.||Interpreting Pie Charts|
|5.||Construction of Pie Charts|
|6.||Solved Examples on Pie Charts|
|7.||Practice Questions on Pie Charts|
|8.||FAQs on Pie Charts|
What are Pie Charts?
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.
Definition of Pie Charts
A pie chart is a type of a 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 represent 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.
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 colours represent the ingredientsused to prepare the cake. What would be the exact quantity of each of the ingredients represented in specific colours 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:
|Quantity of Flour||30|
|Quantity of Sugar||20|
|Quantity of Egg||40|
|Quantity of Butter||10|
Uses of Pie Charts
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.
Let us learn the formula of a pie chart and the method to calculate a pie chart.
Pie Charts Formula
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°
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 ice creams -(10/20)× 100 = 50%
Amount spent on toffees - (4/20)× 100 = 20%
Amount spent on popcorn - (2/20)× 100 = 10%
Amount spent on ride - (4/20)× 100 = 20%
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%
Interpreting Pie Charts
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?
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
Construction of Pie Charts
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
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°
|Mango||(45/150) × 360||108°|
|Orange||(30/150) × 360||72°|
|Plum||(15/150) × 360||36°|
|Pineapple||(30/150) × 360||72°|
|Melon||(30/150) × 360||72°|
With all the above degrees, with the help of a protractor draw a pie chart. Thus, the pie chart looks like this:
Listed below are a few interesting topics that are related to the concept of a pie chart, take a look!
Solved Examples on Pie Charts
The following chart shows the various activities done by Diana in a week.
a) Calculate the central angle subtended at sleeping.
b) Find the portion of time spent by Diana at school.
c) Find the central angle subtended in playing.
a) Time spent in sleeping = 34%; (34/100) × 360 = 122.4°. Therefore, the central angle subtended at sleeping = 122.4°
b) Time spent at school = 25%; 25/100 = 1/4. Therefore, she spends 1/4th of her time in school.
c) Time spent on playing = 8%; (8/100) × 360 = 28.8°. Therefore, the central angle subtended at playing = 28.8°
Example 2: The pie chart shows the favorite subjects of students in a class. Using the information given in the pie chart, find the the percentage of students who chose English.
Let's first determine the percentage of students who chose English by looking at the pie chart.
We know that 144° + 36° + 72° + 108°= 360°
The percentage of students who chose English: (72/360) × 100 = 20
Therefore, the percentage of students who chose English = 20%
FAQs on Pie Charts
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.
How do we Construct Pie Charts?
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°