Previously, we examined censuses and surveys. We get the best data from a census because it includes the entire population. However, it's not always possible to conduct a census, so we often get our data from surveys instead.

Ideas

Surveys

Surveys

When we take a survey it is important that the results are representative of the population. This means that the results that we get for any question we ask of the survey would be the same as if we asked it of a census. This also means that the mean, median, mode and range of the survey should be very close to the same results of the census (although getting exactly the same results is almost impossible).

If a survey is not representative, we call it biased. There are a number of potential sources of bias that we should avoid:

Consider who is being surveyed. If the people being surveyed do not resemble the population, the survey is likely to be biased. For example, surveying train travellers about their opinions on public transport will likely give very different results than a census of the entire population.
Also consider how many people are being surveyed. Asking one person's opinion will not tell you anything about anyone else's opinion. In general, the bigger the number of people being surveyed, the closer the results will be to a census.
Make sure that the questions being asked actually address the question at hand. For example, asking, "Do you approve of the current governing party?" does not give the same results as asking, "Will you vote for the current governing party in the next election?"
Avoid questions which use emotive language or might otherwise influence the results of the survey. For example, asking, "Do you watch the most popular sport, soccer?" will be biased unlike asking, "Do you watch soccer?". These are referred to as "leading questions" as they lead the person being surveyed to a particular answer.

Examples

Example 1

Consider the following questions and determine why they are inappropriate for a survey.

"How many large electronic devices are in your home?"

Question is unclear.

Emotional language.

Should be a "yes" or "no" question.

Question is too personal.

Worked Solution

Create a strategy

Think about how you would feel if someone asked you this question. Would you feel confused on what is being asked? Would you feel it is difficult to answer?

Apply the idea

The question shows an ambiguity by stating large electronic devices which is not specific. So the correct answer is option A.

"Many people have worked incredibly hard and even died making this bridge. Do you like it?"

Question is unclear.

Emotional language.

Should be a "yes" or "no" question.

Question is too personal.

Worked Solution

Create a strategy

Think about how you would feel if someone asked you this question. Would you feel confused? Would you feel pressured to give one answer more than the other?

Apply the idea

The question evokes an emotional reaction by stating that many people have worked hard and even died making the bridge. So the correct answer is option B.

Example 2

Consider each survey question and the sample used and determine whether the outcomes are likely to be biased or not.

Rosey is asking people on her soccer team, "What's your favourite sport?"

Worked Solution

Create a strategy

Consider who is being surveyed.

Apply the idea

Since the question being asked is about the favourite sport, the soccer team will probably answer soccer since they play it. So the outcomes are likely to be biased.

James randomly selected people from his school to find about the school sports. He asked "What's your favourite school sport?"

Worked Solution

Create a strategy

Consider who is being surveyed and whether the question is leading.

Apply the idea

James randomly selected students so there is no bias with the system. The question is not leading. So the outcomes are not likely to be biased.

Gwen randomly selected people from her school and asked, "The local AFL team is donating money to our school this term. What's your favourite sport?"

Worked Solution

Create a strategy

Consider whether the question is leading.

Apply the idea

The question uses leading language by stating the donation of the local AFL team, so people may feel pressured to choose AFL. So the outcomes are likely to be biased.

Example 3

A survey asks the following two questions with the results displayed.

Do you prefer reading, watching TV, or gaming?

Reading	Watching TV	Gaming
23	21	35

Do you prefer studying, cleaning, or exercising?

Studying	Cleaning	Exercising
12	8	59

What statement can be made from the results shown?

Students would rather exercise than clean.

Most students would rather be exercising than gaming.

Students exercise around seven times more than they clean.

Most students don't like watching TV.

Worked Solution

Create a strategy

Consider which options are being compared in each question.

Apply the idea

The survey only allows us to compare the three activities in one question at a time. So we don't know how the activies compare outside of the 2 groups. So options B and C are incorrect.

The questions asked what activity people preferred, not if they liked each activity. So option D is incorrect.

Since exercise and cleaning are in the same group and more people in that group chose exercising, option A is correct.

Idea summary

There are a number of potential sources of bias that we should avoid:

Consider who is being surveyed. If the people being surveyed do not resemble the population, the survey is likely to be biased.
Also consider how many people are being surveyed. Asking one person's opinion will not tell you anything about anyone else's opinion.
Make sure that the questions being asked actually address the question at hand.
Avoid questions which use emotive language or might otherwise influence the results of the survey.

11.06 Surveys

Introduction

Ideas

Surveys

Examples

Example 1

Example 2

Example 3

Outcomes

MA4-20SP

What is Mathspace

About Mathspace