We've already looked at categorical data, which is data that is sorted by groups or categories. Now we are going to look at how we can use this information to draw conclusions or decisions about a data set.

Let's see how with an example.

$50$50 people were asked to choose their favourite types of movies and their results are displayed in the bar chart below.

Discuss

What conclusions can you draw from the graph? e.g. What is the least popular type of movie?
If you owned a cinema complex and you could only show 2 types of movies, which 2 types would you pick? Why?

Researchers and businesses use data, such as surveys of people's preferences for one product over another, to help shape the decisions they make as this kind of information can be very powerful!

Explaining Results

Tables and graphs are an excellent way to display results visually. However, we may also want to use percentages, fractions or decimals to explain how common a particular choice is. For example, if $18$18 out of $24$24 people in a Year 6 class said dogs were their favourite kind of animal, we could write this as a fraction as $\frac{18}{24}$1824, which we could simplify to $\frac{3}{4}$34. Then we could write up a fun report!

Dogs: truly year 6 students' best friends

A recent survey showed that $\frac{3}{4}$34 of Year 6 students picked dogs as their favourite kind of animal. This was far more than any other type of animal...

Let's look at some more examples now.

Worked Examples

Question 1

A restaurant owner recorded how many employees arrived early, on time or late.

Complete the table.

Arrival Tally Frequency

Early ~~||||~~ ~~||||~~ $\editable{}$

On-Time ~~||||~~ ~~||||~~ ~~||||~~ ~~||||~~ || $\editable{}$

Late ~~||||~~ || $\editable{}$
How many employees did the restaurant owner survey in total?
When did the majority of employees arrive?
Late.
A
On-time.
B
Early.
C
Complete the column graph using the results from the table above.

Arrival	Tally	Frequency
Early	~~\|\|\|\|~~ ~~\|\|\|\|~~	$\editable{}$
On-Time	~~\|\|\|\|~~ ~~\|\|\|\|~~ ~~\|\|\|\|~~ ~~\|\|\|\|~~ \|\|	$\editable{}$
Late	~~\|\|\|\|~~ \|\|	$\editable{}$

Question 2

Students were asked to name their favourite subject at school. Their answers are displayed in the pie chart.

Which of the following subjects is more popular?
$English$
A
$Maths$
B
Which subject is most popular in the school?
Other
A
$History$
B
$Science$
C
$Maths$
D
$English$
E
What fraction do the students that prefer $English$ represent?

Question 3

The bar graph shows the number of each type of car fixed by the local mechanic.

Which car brand does the mechanic fix most often?
$Mercedes$
A
$Toyota$
B
$Mitsubishi$
C
$Holden$
D
$BMW$
E
Which car brands did the mechanic fix equally as often?
$Mitsubishi$
A
$BMW$
B
$Toyota$
C
$Holden$
D
$Mercedes$
E
What fraction of the total number of cars do $Toyota$ s represent?

Outcomes

S3-1

Conduct investigations using the statistical enquiry cycle: – gathering, sorting, and displaying multivariate category and wholenumber data and simple time-series data to answer questions;– identifying patterns and trends in context, within and between data sets; – communicating findings, using data displays

Categorical Data II (collecting and displaying)