Topics
14. Data
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AustraliaNSW
Stage 3

14.06 Horizontal bar graphs and vertical column graphs

Lesson
Practice
Lesson

Are you ready?

Can you read information from  dot plots  ?

Examples

Example 1

The following dot plot shows the number of students in each section of the school band:

A dot plot titled band members showing the members in each section. Ask your teacher for more information.
a

Which section has the least members?

A
Percurssion
B
Woodwind
C
Brass
D
Strings
Worked Solution
Create a strategy

Choose the section with least of dots.

Apply the idea

Looking at the dot plot, percussion has the least dots.

So the correct answer is option A.

b

How many people are in the band?

Worked Solution
Create a strategy

Count all the dots for each section, and then add the results together.

Apply the idea

Each dot represent 1 person.

\displaystyle \text{Total dots}\displaystyle =\displaystyle 8+7+5+3Add the dots for each section
\displaystyle =\displaystyle 23

So there are 23\,people in the band.

c

How many more people are there in the Strings section than the Brass section?

Worked Solution
Create a strategy

Subtract the number of dots for the brass section from the number of dots for the strings section.

Apply the idea

Each dot represent 1 person.

\displaystyle \text{Difference}\displaystyle =\displaystyle 8-5Subtract the brass dots from the string dots.
\displaystyle =\displaystyle 3

So there are 3 more people in the Strings section than in the Brass section.

Idea summary

Dot plots show us how many of something, using dots. The key is really important, because it tells us if each dot is worth 1, or more than 1.

Create and interpret column graphs

This video uses a number of column graph examples and explores some strategies about how to interpret them.

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Examples

Example 2

This table shows the number of badges five students sold for a local charity.

StudentsNumber of badges
\text{Derek}70
\text{William}65
\text{Frank}75
\text{Sandy}60
\text{Tara}65
a

Create a column graph which shows the number of badges by student.

This image shows an empty graph about number of badges sold by 5 students. Ask your teacher for more information.
Worked Solution
Create a strategy

Use the table to know how high each column should go.

Note that the ticks on the vertical axis go up by 5s not 1s.

Apply the idea

When drawing each column, the tick for the name should be in the center of the column. Each column should be the same width. There should be gaps between each column.

From the table, Derek sold 70 badges. So the column above Derek's name should go up to 70. We can use the same method for the rest of the columns.

The column graph shows the number of badges 5 students sold. Ask your teacher for more information.
b

Which student sold the same number of badges as Tara?

A
Frank
B
Derek
C
William
Worked Solution
Create a strategy

Look for another column which has the same height as Tara's column.

Apply the idea

Looking at the column graph, we can see that William's column has the same height as Tara's.

So the correct answer is option C.

Idea summary

When drawing a column graph, the tick for the category should be in the center of the column. Each column should be the same width. There should be gaps between each column.

The height of the column is equal to the number of times that category occurs.

Horizontal bar graphs

This video introduces horizontal bar graphs as an avenue for displaying and interpreting data.

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Examples

Example 3

The bar graph shows the merit points received by four students in a class.

A horizontal bar graph showing the number of merit points for 4 students. Ask your teacher for more information.
a

How many points in total were earned by Tari and Emily?

Worked Solution
Create a strategy

Add the points that the two columns reach.

Apply the idea

Tari's bar goes up to 10 so she earnt 10 points. Emily's bar goes up to 8 so she earnt 8 points.

\displaystyle \text{Total points}\displaystyle =\displaystyle 10 + 8Add the points
\displaystyle =\displaystyle 18
b

How many more points did Nayan earn than Ivan?

Worked Solution
Create a strategy

Subtract Ivan's points from Nayan's.

Apply the idea

Nayan's bar goes up to 16 so he earnt 16 points. Ivan's bar goes up to 12 so he earnt 12 points.

\displaystyle \text{Difference}\displaystyle =\displaystyle 16-12Subtract Ivan's points from Nayan's
\displaystyle =\displaystyle 4

So Nayan earned 4 more points than Ivan.

Idea summary

A horizontal bar graph works in a similar way to a vertical bar graph, but the axes are switched around. The category is on the left axis, and the results are on the bottom axis. Instead of seeing how tall a bar is, we look at how far to the right the bar extends.

Side by side column graphs

This video shows how side by side column graphs can be used to compare two sets of similar data.

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Examples

Example 4

A survey was conducted about people's favourite movie genre. The results were plotted in the column graph below.

The image shows a side by side column graph about movie genres. Ask your teacher for more information.
a

Complete the frequency table with the information.

ComedyActionDramaHorror
Women305
Men4020
Worked Solution
Create a strategy

Use the colour key to find the number of men and women that like each genre by comparing the heights of each column to the number on the vertical axis.

Apply the idea

We can see that the darker blue column is for women, while the lighter blue column is for men. Using this, we can find the number that matches the top of each column.

For Drama, the dark blue column goes up to 45 and the light blue column goes up to 10. So 45 women and 10 men like drama. We can use the same process to complete the table.

ComedyActionDramaHorror
Women3020455
Men30401020
b

Which genre had the same number of men and women select it as their favourite?

Worked Solution
Create a strategy

Find the genre with the same number in the completed frequency table from part (a).

Apply the idea

From the table, the same number of men and women selected Comedy as their favourite.

Idea summary

Column graphs can be vertical or horizontal, but we can also use side-by-side graphs to dig a little deeper into our data. Instead of showing a total, we can split it into categories to compare data.

Outcomes

MA3-18SP

uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

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