Session 3: What is Bar Graph? – Definition, Reading, Interpretation, Steps and Examples

In the previous lesson ‘What is a Pictograph?’, we have seen that representing data by pictograph is time-consuming and tricky. Though pictographs make the data more visually interesting, memorable, or engaging, it is also difficult to represent the exact value of data using this graph. There is an alternative method to represent numerical data by using rectangular bars. This method is called a bar diagram or a bar graph. 

In this lesson, we will briefly look into reading, interpreting, and constructing a bar graph.

What is a Bar Graph?

A bar graph is a pictorial representation of the numerical data with rectangular bars. The graph usually compares different categories. Although the graphs can be plotted vertically (bars standing up) or horizontally (bars laying flat from left to right), the most usual type of bar graph is vertical. In the construction of both these forms, the height or length of the bar indicates the corresponding value of the numerical data on a suitable scale. The width of the bars is not governed by any set rules. Regarding the space between two bars, it is conventional to have space about one-half of the width of a bar. 

Reading and Interpretation of Bar Graphs

When you know how to read a bar graph, you can learn a lot about the items being compared. The first step of reading a bar graph is to know the title, which is usually at the top. The title of the graph provides a general overview to the reader of what is being measured and compared. Next, we read the labels written just below the x-axis and adjacent to the y-axis. After knowing what the bar graph represents, we read the scale, which is the set of numbers along the axes of the graph. These help us see the precise values in the given data. 

After reading a bar graph, the data lead us to discussions and conclusions. 

1) Read the bar graph shown below and answer the following questions. 

i. In which month was the precipitation maximum?

First, look at the horizontal bars on the graph and find the longest bar. The longest bar is the one that extends farthest to the right. Then, look to the left of this longest bar to see the month represented by this bar. 

The answer is July. 

ii. What was the average precipitation for the month of June?

First, look on the vertical axis and find the month of June. Next, follow the horizontal bar for this month to the right until you reach the end of the bar. Then, find the value on the horizontal axis labelled ‘Average Precipitation (mm)’ that corresponds with the end of the bar. 

The answer is 80 mm. 

iii. Which month had the lowest average precipitation?

First, look at the horizontal bars on the graph and find the shortest bar. The shortest bar is the one that extends least to the right. Then, look to the left of this longest bar to see the month represented by this bar. 

The answer is May and October. 

What is a Double Bar Graph?

A bar graph is used to display one set of data using single bars of various heights. A double bar graph is used to display two sets of data on the same graph. A double bar graph helps us compare or present more than one kind of information, situation or event by using two bars beside each other at various heights. A double bar graph has two axes. One axis of a double bar graph shows the categories being compared, and the other represents the scale. It is important to know that all double bar graphs must have a title and a key. The key for a double bar graph will represent the groups being compared with two different colours. 

2) The following bar graph displays the temperature in degrees Celsius for the first week of April for 2019 and 2020, respectively. Use the bar graph to answer the questions presented below the graph. 

i. What was the highest recorded temperature in the year 2019?

First, look at the bar graph to determine which colour bar represents 2019. Next, look at the temperatures above each bar for 2019 and record the highest number. 

The answer is 39°C. 

ii. What is the lowest temperature recorded for the year 2020?

Look at the bar graph to determine which colour bar represents 2020. Next, look at the temperatures above each bar for 2020 and record the lowest number. 

The answer is 30°C.

iii. What is the average daily temperature for the week displayed on the bar graph for each year?

First, begin with 2019 and record the seven temperatures displayed on the bar graph. Next, calculate the sum of the recorded temperatures. Then, divide the sum by the number of days to determine the average daily temperature. 

Average for the year 2019=.

Next, repeat the same steps for the year 2020. 

Average for the year 2020=. 

How to Draw a Bar Graph?

To draw a graph, we draw two mutually perpendicular lines. The horizontal line is called the x-axis, and the vertical line is known as the y-axis. If the bars are drawn vertically on the x-axis then the height of the bars is shown along the y-axis. If bars are drawn horizontally on the y-axis then the length of the bars is shown along the x-axis. Axes always need to be labelled to show what each axis represents. 

While constructing the bar graph, the following points should be kept in mind:

• The width of the bar is arbitrary and is equal for all the bars. 
• The height (or length) of each bar is proportional to the corresponding frequency. 
• The space between each bar is uniform. 

3) The following table gives the heartbeat rates for different animals. The heartbeat rate is stated in beats per minute. 

Animal	Pig	Elephant	Cow	Giraffe	Whale	Dog
Heartbeats	70	30	65	65	20	75

Represent the above data by a bar graph. 

To represent the above data by a bar graph, we first draw a horizontal and a vertical line. Along the x-axis, mark animals and along the y-axis, mark the number of heartbeats per minute. Since six values of the numerical data are given, we mark six points on the horizontal line at equal distances and draw bars of the same width at these points. The height of the bars for different animals will be proportional to the number of heartbeats. Now we choose a suitable scale to determine the height of the bars, according to the space available. Here, we choose 1 division to represent ten heartbeats. 

Now, we calculate the length of the bars as follows:

The length of the bar for pig=\(\frac{70}{10}\)=7 divisions.  

The length of the bar for elephant=\(\frac{30}{10}\)=3 divisions. 

The length of the bar for cow=\(\frac{65}{10}\)=6.5 divisions.

The length of the bar for giraffe=\(\frac{65}{10}\)=6.5 divisions.

The length of the bar for whale=\(\frac{20}{10}\)=2 divisions.

The length of the bar for dog \(\frac{75}{10}\)=7.5 divisions.

We draw the bars keeping the width of each bar uniform. It may be of any measure. 

The vertical bars above compare the average heartbeat per minute for six animals. This same bar graph can also be displayed using horizontal bars, as shown below. 

Steps to Construct a Bar Graph

We can use the following steps to construct a bar graph from the given data:

Step 1: On the graph, draw two perpendicular lines – horizontal axis and vertical axis and label them. 

Step 2: Along the horizontal (or vertical) axis, choose the uniform width of the bars and the uniform space between them. 

Step 3: Choose a suitable scale to determine the height (or length) of the bars, according to the space available. 

Step 4: Calculate the height (or length) of various bars and draw them on the graph. 

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What is a Bar Graph? – Examples

Example 1

The following bar graph represents the results of a survey to determine the type of TV shows watched by high school students. 

Use the bar graph to answer the following questions:

i. What type of show is watched the most?

Sit-coms are watched the most.

ii. What type of show is watched the least?

Quiz shows are watched the least.

iii. Approximately how many students participated in the survey?

Approximately 45+20+18+6+35+16=140 students participated in the survey.

iv. Does the graph show the differences between the preferences of males and females?

No, the graph does not show the differences between the preferences of males and females.

Example 2

The below-given double bar graph displays the number of boys and girls who have a favourite sport.

Use the double bar graph to answer the following questions.

i. What is the difference between the number of boys and the number of girls who chose the track as their favourite sport.

First, we find the sport being asked about. In this case, it is the track.

Next, compare the number of boys and girls who like track by comparing the blue and the pink bars representing track data. Five girls and two boys chose the track as their favourite sport.

Subtract the data to find the difference between the two. Because more girls chose track than boys, we subtract the number of boys from the number of girls.

5−2=3

The answer is 3.

ii. What is the favourite sport of girls?

First, look at the key to determine which colour bar represents girls’ favourite sports. Next, look at the number above each bar for girls and record the highest number.

The answer is tennis.

iii. What is the least favourite sport of boys?

First, look at the key to determine which colour bar represents boys’ favourite sports. Next, look at the number above each bar for boys and record the lowest number.

The answer is the track.

iv. Which sport is liked equally by both boys and girls?

We find the two bars on the graph that line up equally with one another. Both the blue and pink will be at the same height on the graph. 

Then look at the x – axis to determine which sport is represented by the equal data among boys and girls.

The answer is cricket. 

Example 3

The following table shows the number of books on different subjects in the library. 

Subject	Physics	Chemistry	Biology	Maths	English	History	Geography	Computers
Number of books	110	115	120	250	200	80	90	70

Draw a bar graph to represent the above data.

Along the x-axis, mark the subjects and along the y-axis, mark the number of books. Since eight values of the numerical data are given, we mark eight points on the horizontal line at equal distances and draw bars of the same width at these points.

Example 4

The data shows how many vegetables Tina grew in her garden in the month of September and October.

September	October
30 carrots	60 carrots
10 tomatoes	20 tomatoes
25 chillis	30 chillis
15 ladyfingers	25 ladyfingers
10 lemons	15 lemons

Help Tina draw a double bar graph to represent the above data.

First, decide on the scale. The range of data is between 10 and 60, so a scale of 0-70 counting by tens is an appropriate scale. Now, along the x-axis mark the vegetables and along the y-axis, mark the number of vegetables. 

Let blue bars represent September and pink bars represent October. This will separate the data, so it does not get mixed up but allows it to be shown in the same graph.

Since five sets of numerical data values are given, we mark points on the horizontal line and draw one category in blue and the other in pink.

  Remember this!

A bar graph is a pictorial representation of the numerical data with rectangular bars. The graph usually compares different categories. A bar graph can include multiple bars for multiple sets of data.