Bar Graphs

A bar graph, also called the bar chart, is a way of representing data graphically in the form of bars. The height of the bars corresponds to the data they represent. Like all graphs, bar graphs are also presented on a coordinate plane having an x-axis and a y-axis.

Parts

The different parts of a bar graph are:

• Title
• Bars
• Categories
• x-axis
• x-axis label
• y-axis
• y-axis label
• Scale

How to Draw a Bar Graph

Let us consider an example. Sam went to the vegetable market and bought some vegetables. He bought 6 kg of potatoes, 8 kg of onions, 5 kg of tomatoes, and 3 kg of capsicum. He now wants to display the data as a bar graph.

To create the bar graph in an excel sheet, he needs to follow the following steps:

1. Giving a title to the graph, for example, ‘Vegetables Bought.’
2. Drawing a horizontal x-axis and a vertical y-axis
3. Labeling the axes: x-axis is ‘Types of Vegetables’, which is an independent variable, and the y-axis is ‘Weights of Vegetables’, which is a dependent variable
4. Labeling the vegetables as potatoes, onions, tomatoes, and capsicum and giving an equal gap between each bar on the horizontal axis.
5. Scaling the graph. For example, it is written as 1 unit = 1 kg
6. Drawing the bars corresponding to the available data.

Following the steps if we draw the above data, the labeled bar graph will look like as given above.

Properties

The key properties of a bar graph are:

1. It represents numerical data by rectangles of equal width but the varying height
2. The height of the bars depends on the value it represents
3. The gap between the bars is uniform
4. It can be vertical or horizontal

Types

Bar graphs are used to represent the frequencies of categorical variables. They are mainly of two types: vertical and horizontal.

Vertical Bar Graphs

Let us assume that Rob has taken a survey of his classmates to find which kind of sports they prefer and noted the result in the form of a table.

When we represent the above data in the form of a vertical bar graph, it shapes up like this:

This form of representation is most commonly used in statistics.

Horizontal Bar Graphs

However, bar graphs can also be presented horizontally. If we represent the above data horizontally, it looks like as shown below:

Sometimes we need to present data representing a group. Such data are presented as either vertical or stacked bar graphs.

Grouped Bar Graph

Also known as the clustered bar graph, it plots numeric values for levels of two categorical variables instead of one side-by-side. Here, the rectangular bars are grouped by position for levels of one categorical variable, with the same colors indicating the secondary category level within each group.

A grouped bar graph can be both vertical and horizontal.

Let us represent the given data in the form of a vertically grouped bar graph.

Number of Students Playing Sports	Golf	Tennis	Football	Rugby	Basketball
Grade 4	6	8	12	10	16
Grade 6	8	10	6	14	5

This is an example of a double bar graph from which we can quickly identify the sport that is most popular of all and the least popular one. It is also used to show the relative sizes of the things under study.

Segmented Bar Graph

Also known as the stacked or composite bar graph, it divides the whole graph into different parts. Each part of the bar represents a particular category with a different color. Thus, a bar represents the whole, and each segment is a part of the whole.

A stacked bar graph can be both vertical and horizontal.

Let us represent the data of a farm producing apples, oranges, bananas, and mangoes for the years 2018, 2019, 2020, 2021, and 2022 in the form of a stacked bar graph.

Production in tonnes	2018	2019	2020	2021	2022
Apple	10	12	8	2	10
Orange	8	6	4	6	4
Banana	2	5	2	8	6
Mango	6	8	10	5	2

What is a Bar Graph Used For

Students widely use bar graphs to represent numeric data in mathematics and statistics. However, it is also used in various industries for business and finance. Some of its uses are:

• Comparison between 2 or more variables is easy
• It is prepared without much effort
• It helps to determine a pattern in data collected over a long period
• Represents data that are grouped into categories. For example, it is used to show the difference in the votes obtained by the winning candidate compared to the rest.
• It also estimates the percentage of some quantity compared to the rest.

Bar Graph vs. Histogram

The main difference is that a bar graph represents ungrouped data. In contrast, a histogram is used to represent grouped data. Again, the bars are not adjacent in a bar graph, whereas in a histogram, the bars are adjacent.  

Solved Examples

E.g.1. Draw a bar graph of the number of students newly admitted to a school in different grades.

Grades	4	5	6	7	8
Number of Students	24	35	16	32	8

Answer:

E.g.2. A survey of 50 students about their favorite season of the year is listed. Prepare a bar graph to show which season is most popular among them.

Seasons	Spring	Summer	Autumn	Winter	Rainy
Number of Students	14	10	7	11	8

Answer:

E.g.3. Draw the horizontal bar graph for the given data set between the number of people and their preferred mode of transport.

Mode of Transport	Bus	Car	Cab	Auto	Walking
Number of People	24	36	48	15	22

Answer:

E.g. 4. Represent the given data in a double-bar graph.

Distance travelled (in km)	Bus	Car	Cab	Auto	Walking
Day 1	6	8	12	10	16
Day	8	10	6	14	5

Answer:

E.g.5. The table shows the number of students newly admitted to St Paul’s and St Xavier’s schools in the following years. Represent your data in the form of a horizontal segmented bar graph.

Number of Students Admitted	2000	2005	2010	2015
St Paul’s	10	12	8	10
St Xavier’s	8	6	4	4

Answer: