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14. Data
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Stage 3

14.02 Surveys

Lesson
Practice
Lesson

Are you ready?

What  types of data  could result from a survey?

Examples

Example 1

What type of data is each of the following:

a

The time spent watching TV each day.

A
Categorical
B
Numerical
Worked Solution
Create a strategy

Determine if the type of data will be words or numbers.

Apply the idea

The data refers to the time spent that is counted or measured using a number.

So the type of data is numerical. So, the correct answer is B.

b

Favourite TV show.

A
Categorical
B
Numerical
Worked Solution
Apply the idea

The data refers to a name of a TV show that is a word.

So the type of data is categorical. The correct answer is A.

Idea summary

If the data contains words it is categorical. If the data contains numbers it is numerical.

Types of questions

This video looks at different types of questions.

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Examples

Example 2

A restaurant manager asks his customers the following question:

“How would you describe the taste of our food?”

a

What type of question is this?

A
Open
B
Closed
Worked Solution
Create a strategy

Think about if there is a variety of possible answers.

Apply the idea

A person can describe taste in a variety of different ways. There is no limit to how it can be described.

So the question is open, option A.

b

To make the question closed, the manager could instead ask:

A
"How would you rate the taste of our food on a scale from 0 to 5?"
B
"How does our food compare to the restaurant next door?"
C
"What did you like most about our food?"
Worked Solution
Create a strategy

Choose a question with limited number of responses.

Apply the idea

Option A has limited possible responses on the scale 0 to 5.

So, the correct answer is Option A.

Idea summary

If our question has a limited set of answers, such as yes/no, red or blue, agree/disagree, it's a closed question. If there is an unlimited number of answers possible, then the question is open.

Survey results

This video shows how survey results can be used and how to be careful about making assumptions.

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Examples

Example 3

Kathleen wants to find out the favourite sport of students at her school. She surveys some students and the results are below.

SportStudent
\text{Tennis}5
\text{Rugby}21
a

According to the survey, which sport is most popular?

A
Tennis
B
Rugby
Worked Solution
Create a strategy

Choose the sport with the largest number of votes.

Apply the idea

Rugby received the largest number of votes at 21.

So, the correct answer is option B.

b

For the survey, Kathleen asked all her teammates from her Rugby team. Do you trust the results of Kathleen's survey?

Worked Solution
Create a strategy

Look at the range of students who were asked in the survey.

Apply the idea

A survey should ask a reasonable number of people from across the group if we are trying to gather information. She asks a range of students from a rugby team, who probably prefer rugby over tennis, then no, we can't trust the survey's result.

Idea summary

When we make a survey, we need to make sure we ask enough people, and choose a variety of people, to answer the questions.

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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