Determine your answers to the following questions about yourself. Choose the answer that fits you best.
- Of these four options, what season do you most prefer?
- Of the flavours listed below, which ice cream flavour do you prefer?
- cookies ‘n’ cream
- I prefer an alternative option
- If you had to choose an animal to research, which of the following animals would you select?
- I prefer an alternative option
- Out of these four options, which of these school subjects would you most enjoy studying?
- science/social studies
- I prefer an alternative option
From this process, what could you learn about others? What could you learn about grade six students? What do you learn about Canadians?
Throughout this learning activity, record your thoughts digitally, orally, or in print.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Populations and samples
Sample and population are words that we may use often, or think we know, but they have specific meanings in terms of math and data collection.
Take some time to brainstorm definitions for population and sample. Record your responses in a format of your choice. When you are finished, press the ‘Hint’ button to reveal definitions to the terms you brainstormed. Compare your answers with the ones provided.
A population is a total set of subjects (can be people, objects, species, or other items) that fit a particular description.
A sample is a subset or small group of subjects that belong to a particular population.
If you were interested in surveying grade six students in Canada, the population would include every single grade six student in Canada, while a sample would be a group of grade six students in Canada.
Usually, surveys share results about a sample, rather than a population.
- Why do you think this may be?
- How do you think samples are able to do this?
- Does it matter who makes up your sample?
Record your responses using a method of your choice.
When you're finished brainstorming, press ‘Suggested Answer’ to check your understanding of the terms and their definitions.
Should samples always be used? Consider the following research questions and decide if it is reasonable to survey the entire population or if a sample should be used. Select the correct answer for each of the questions.
Create your own questions
Now that you’ve seen some examples, come up with a few questions of your own. When would researchers want to survey a sample vs. a population? Record your questions in the fillable Sample and Population Table or using a method of your choice.
Press the ‘Activity’ button to access Sample and Population Table.
There are a variety of sampling methods that can be used to create a representative sample of the population. Why do you think it is important that a sample be representative of the population? Press the ‘Hint’ button to reveal an example.
There are three methods of creating a sample for surveying.
Individuals are randomly selected from the population to be surveyed, and everyone has the same chance of selection.
A population is divided into subgroups based on a common characteristic and then a random sample is taken from each group.
A starting point and an interval, such as a chosen age range, are randomly chosen and then the sample is systematically selected based on that interval.
Which method do you think is the best? Why might stratified random sampling be used? Why might systematic random sampling be used?
Examples of samples
Explore the following survey.
Research question: What do students in Country A want to be when they grow up?
Sample: 50 Kindergarten students from schools across City A.
What do you notice about the results of this survey? Respond to the following questions in the method of your choice.
- Do you think the results would be different if you asked a different grade of students in City A?
- What if you asked another group of Kindergarten students in a different city or province?
- What if you asked the same group of students 7 years from now?
- Do you think the sample of 50 kindergarten students in City A represents the population of all students in Country A? Why or why not?
Press ‘Hint’ to reveal example responses.
This sample provides biased survey results to the research question. Kindergarten students have very different interests, understandings, and expectations about their futures and possibility of jobs than students in different grades. For example, students in grade ten would probably have vastly different answers!
Further, students in other cities or provinces might have completely different ideas of job possibilities based on the jobs they more commonly see around them. This means that the results are biased. Bias means that the results of a survey are not likely to apply to the rest of the group or population that they are intended to.
Investigate the examples below and determine if they are fair or biased. If they are biased, what factors might impact the results?
- Research question: How old are most Canadians when they are first introduced to technology?
Sample: 150 20-year old’s in a neighbourhood in Vancouver.
|Eight to 10|
|10 to 15|
|15 to 20|
- Research question: What is the preferred winter activity for children aged eight to 12 in Canada?
Sample: 500 children randomly selected from all over Canada
- Research question: What is the most common method of transportation used to get to work?
Sample: 350 young adults in Toronto.
Press ‘Hint’ to reveal the sample answers.
- I think this sample is biased because they are asking only people in one city to determine the age of most Canadians. The sample is also not very large. As well, they are only asking one age group.
- I think this is a fair sample since a good number of random children were asked all over Canada. I think it would be even more fair if the children were 8 to 12 years old.
- I think this is a biased sample. They are only asking one age group and they are asking them in a big city. It might look very different in smaller cities and towns, especially where there isn’t a subway, and if they asked older people, the results might look different. I think this would be a fair sample if the question were: What is the most common method of transportation for young adults in Toronto?
Task 1: A survey for a population
Create a survey question for a population that you are interested in learning about. Determine a fair sample of that population and develop a plan for surveying them. You do not need to actually conduct your survey. Answer the following questions in a method of your choice.
- How would you conduct your survey?
- What type of data would you need to gather?
- How would you record the results?
- How can you ensure that your survey is not biased?
Task 2: Reflection
Reflect on and answer the following questions:
- Why is it important for a survey to be unbiased?
- What are the pros and cons of surveying a whole population? A sample?
- How does the sample that you choose affect the results of your survey?
As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.
Now, record your ideas using a voice recorder, speech-to-text, or writing tool.
Press ‘Discover More’ to extend your skills.Discover More
A census is a type of survey that attempts to collect data from an entire population. The goal of a census is to determine demographic, social and economic information about the people living all over Canada. It reports about information from every household that is important to a country and can help governments, businesses, associations, and community organizations to make decisions.
Canada conducts a census every five years. Research Canada’s most recent census (2016). Click on a few different cities/towns and explore the types of questions asked. Notice how the data is organized and categorized.
What can you learn from exploring the results of a census? Why do we administer a census? What data can be collected?
Connect with a TVO Mathify tutor
Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.TVO Mathify (Opens in a new window)