# Bar Graphs

Peter wanted to arrange the birthdays of his classmates according to their months.

He then wants to display the data in a way that he can visually understand them.

This is where he faces a problem.

He doesn't want to use a pictograph since it takes too much time also might be difficult.

He wants to do it in an easier method.

Can you suggest a better option for Peter?

Bar graphs can help him represent the data using rectangular bars, aiding better visualization.

In this chapter, we will learn about the types of bar graphs and double bar graphs. Check out the interactive simulation to know more about the concept of Bar Graph/ Bar Chart and try your hand at solving a few interesting practice questions at the end of the page.

**Lesson Plan**

**What is Bar Graph?**

**Bar graph **is a specific way of representing data using** rectangular bars** where the length of each bar is proportional to the value they represent.

Bar graphs are the pictorial representation of grouped data and are also referred to as b**ar charts**.

Bar graphs are one of the examples of data handling.

Bar graphs are an excellent tool when representing data that are independent of one another and don’t need to be in any specific order while being represented.

The bars provide a visual display for comparing quantities in different categories.

The graphs can be plotted vertically (bars standing up) or horizontally (bars laying flat from left to right), but normally we use vertical bars.

**Example:**

Liza went to the market for buying different types of fruits. She then wants to display the data in a way that she can visually understand which type of fruits she buys the most.

We can start by counting each type of fruit and putting the data in a table.

Types of Fruits |
Number of Fruits |
---|---|

Apples |
5 |

Mangoes |
3 |

Watermelons |
2 |

Strawberries |
3 |

Oranges |
6 |

Let’s represent the data given below using a bar graph.

Now, the above bar graph shows the different types of fruits and the number of fruits bought by Liza.

From the above graph, we can easily say that orange is the type of fruit that Liza buys the most by looking.

This is the advantage of bar graphs.

**Properties of Bar Graph**

- All bars must be of equal width.
- The bars can be drawn horizontally as well as vertically as per your needs.
- The height of the bar is proportional to the data they represent.
- All bars must share a common base.

**Types of Bar Graphs**

To presenting the data visually, there are several different types of bar graphs we can consider.

There are different types of bar graphs and they are as follows:

- Vertical bar graph
- Horizontal bar graph

**1. Vertical Graph**

The most common type of bar graph is the vertical bar graph. It is very useful when representing a series of data over time.

"The bar graphs that represent the grouped data vertically are called vertical bar graphs."

The horizontal (x)-axis represents the categories and the vertical (y)-axis represents the data value for those categories.

This is how a vertical graph looks like:

**2. Horizontal Graph**

"The bar graphs that represent the grouped data horizontally are called horizontal bar graphs."

The data categories are shown on the vertical axis and the data values are shown on the horizontal axis.

This is how a horizontal graph looks like:

**Double bar graph**

A **double bar graph** is just like a normal bar graph. The only difference is that it is used to compares 2 data groups.

In other words, a double bar graph is a graphical representation of information using two bars beside each other at various heights.

The bars can be arranged vertically or horizontally.

It is also referred to as double bar charts.

For example:

The sales of English and Science books in the years 2008, 2009, 2010, 2011 and 2012 are given below in the table:

Years |
2015 |
2016 |
2017 |
2018 |
2019 |
---|---|---|---|---|---|

English |
30 |
35 |
20 |
25 |
40 |

Science |
20 |
40 |
25 |
35 |
20 |

Let’s represent the data given above using a double bar graph.

- If the frequency of data is very large, then bar graphs are always advisable since pictographs become time-consuming and very difficult to make.
- There is one disadvantage of vertical bar graphs is that they don't leave much space at the bottom of the chart if long labels are required to write.

**How to Draw a Bar Graph?**

The following steps must be followed while drawing a bar graph:

**Step 1:** First, draw a horizontal and a vertical line( i.e. the x-axis and y-axis ).

**Step 2:** Sort the data collected according to the category.

Make a table to build a bar graph.

Class |
Number of Girls |
---|---|

Class 5 |
30 |

Class 6 |
35 |

Class 7 |
20 |

Class 8 |
25 |

Class 9 |
40 |

**Step 3:** Choose a scale. The scale represents how much of the data is represented by a unit length of the bar.

And label the x-axis & y-axis.

**Step 4:** Now, draw the bar with heights corresponding to the value of the data.

**Uses of Bar Graph**

A bar graph or bar chart is a pictorial representation of data. It is mostly used in maths and statistics.

Some of the uses are as follows:

- A bar graph makes comparisons between different variables easy and convenient.
- Bar graphs are also the easiest diagram to prepare. They do not require too much effort.
- Bar graphs are the most widely used method of data representation. They are used in various industries.
- Bar graphs are used to compare data sets that are independent of one another.
- They help in analyzing patterns over long periods of time.

**Make a Bar Graph**

Test yourself by trying out the simulation given below:

**Solved Examples**

Example 1 |

The number of children in five different batches of an educational institute is given below.

i) Represent the data on a bar graph.

Batches |
Number of Children |
---|---|

Batch 1 |
120 |

Batch 2 |
80 |

Batch 3 |
95 |

Batch 4 |
100 |

Batch 5 |
60 |

ii) Find the ratio of students of Batch 1 to the students of Batch 3

**Solution**

i) The data is represented by the bar graph is as follows:

ii) Number of students in Batch 1 = 120

Number of students in Batch 3 = 95

\(\begin{align}\frac{\text{Number of students in Batch 1}}{\text{ Number of students in Batch 3}}&=\frac{120}{95}\\&=\frac{6}{5}\end{align}\)

\(\therefore\) The Ratio is = \({ 6: 5 }\) |

Example 2 |

Observe this bar graph which is showing the baking of cakes in a bakery from Monday to Saturday.

Answer the following question:

On which day were the maximum cakes were baked? How many cakes were baked on that day?

**Solution**

From the above graph, it is shown that

On Saturday the maximum cakes were baked.

60 cakes were baked on that day.

\(\therefore\) Maximum cakes on Saturday = \({ 60 \text{ cakes}}\) |

Example 3 |

The following table shows the number of apple trees planted by the Gardener of a school in different years.

Years |
Number of apple trees |
---|---|

2005 |
150 |

2006 |
220 |

2007 |
350 |

2008 |
150 |

2009 |
300 |

2010 |
380 |

Draw the bar graph to represent the data.

**Solution**

The data is represented by the bar graph is as follows:

Example 4 |

The number of cars manufactured by a factory for five consecutive weeks is shown below:

Week | Number of Cars |
---|---|

First |
600 |

Second |
850 |

Third |
700 |

Fourth |
300 |

Fifth |
900 |

I) Draw a bar graph to represent the data.

II) How many cars were manufactured on week third?

**Solution**

i) The data is represented by the bar graph is as follows:

ii) From the above graph, it is shown that

Number of cars were manufactured on week third = 700

\(\therefore\) Number of cars on week third = \({ 700 \text{ cars}}\) |

Example 5 |

The data collected from a survey of a city is given below.

Draw a double bar graph, choosing the appropriate scale, and answer the following:

Sports |
\(\text{Foot}\) ball |
\(\text{Base}\) ball |
\(\text{Basket}\) ball |
Tennis |
Golf |
---|---|---|---|---|---|

Watching |
1200 |
570 |
700 |
500 |
400 |

Playing |
800 |
400 |
350 |
400 |
105 |

What is the average number of watching sports per person?

**Solution**

The data is represented by the double bar graph is as follows:

Average of watching sports

\(\begin{align}&= \frac{(1200 + 470 + 510 + 430 + 250)} {5}\\&= \frac{2860}{5}\\&= 572 \end{align}\)

\(\therefore\) Average number of watching sports\({ = 572 }\) |

- To solve the questions on the bar graph, first, understand the data presented on the x-axis and y-axis and what's the relation between the two in terms of length bars.
- There must be equal spacing between the bars.

**Interactive Questions**

**Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.**

**Let's Summarize**

We hope you enjoyed learning about the Bar Graph/ Bar Chart with the simulations and practice questions. Now you will be able to easily solve problems on types of bar graph, and double bar** **graph**.**

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**Frequently Asked Questions ****(FAQs)**

## 1. What are vertical and horizontal bar graphs?

The bar graphs that represent the grouped data vertically are called vertical bar graphs.

The data categories are shown on the horizontal axis and the data values are shown on the vertical axis.

The bar graphs that represent the grouped data horizontally are called horizontal bar graphs.

The data categories are shown on the vertical axis and the data values are shown on the horizontal axis.

## 2. What is a line graph?

A line graph is a type of chart or graph which is used to shows information when a series of data is connected by a line.