DoAssignment study guide

D1.1 · Choose one-variable or two-variable data for a question

Learn to choose one-variable or two-variable data for a question through clear examples and targeted practice.

Ontario Grade 8 Mathematics

Data

Match the information you collect to the question you want to answer

Suppose a class wants to learn about students’ ways of getting to school. If the question is “How do students get to school?”, each student needs to give one kind of information: a way of travelling. If the question is “Does travel time differ by way of travelling?”, each student needs to give two connected pieces of information: a way of travelling and a travel time. The question determines what data to collect. In this lesson, data means information collected to answer a question. A variable is a characteristic that can have different recorded values, such as a travel method or a time. The goal is to choose the right number of variables—not to collect extra information just because it might be interesting.

What you will learn

Identify what a question is asking you to find out.
Choose one-variable data when a question asks about one characteristic.
Choose two-variable data when a question asks about a possible relationship between two characteristics.
Explain why the chosen data fit the question.

Start with the question

Before collecting data, read the question carefully. Ask: What information would I need from each person, object, or event to answer it? Each distinct characteristic you record is a variable. A response such as “walking” or “bus” is a value of the travel-method variable.

A question may ask for a count or a description of just one characteristic. For example, “Which school club do students prefer?” asks about club preference. Each student gives one club choice. The data have one variable, even though the possible answers include many different clubs.

Do not decide based on how many possible answers there are. One variable can have many possible values. Instead, count the kinds of information needed from each person or item.

A variable is one characteristic that is recorded.
Many possible values can still belong to one variable.
Use the question to decide what information is needed.

When one-variable data fit

Choose one-variable data when the question is about a single characteristic. Examples include “What is the most common way students travel to school?” and “How many books did each student read last month?” In the first question, the recorded characteristic is travel method. In the second, it is number of books read.

A one-variable list gives one recorded value for each person or item. You can then describe that characteristic, such as which response appears most often. For this lesson, focus on choosing the data that fit the question; the key decision is that only one characteristic is needed.

A useful check is to imagine one row of your planned records. If one answer from each person is enough to address the question, one-variable data may fit. Be sure the question itself does not ask how one characteristic changes with, or is connected to, another.

One-variable data record one characteristic for each person or item.
The number of response choices does not determine the number of variables.
A question about one characteristic usually needs one variable.

When two-variable data fit

Choose two-variable data when the question asks about a possible connection between two characteristics. Each record must keep both values together for the same person, item, or event. These are paired data: two values linked because they belong to the same case.

For example, to ask whether students who spend more time practising an instrument also tend to report more practice sessions, you would need practice time and number of sessions for each student. Recording practice time for one group and session counts for a different group would not create paired data. You could not tell which two values belonged together.

A two-variable question asks about both characteristics, not merely for two unrelated facts. “What are students’ favourite sports and favourite foods?” could collect two answers, but unless the question asks how the answers are connected, it may simply be two separate one-variable questions. State the purpose clearly before choosing what to record.

A scatter plot can show paired numerical data as dots. Each dot stands for one case and shows that case’s two values. A plot can help people notice a possible pattern, but the plot alone does not explain why a pattern appears. Choose two-variable data only when the question needs information about two characteristics together.

Two-variable data record two characteristics for each same case.
Keep the two values paired so their connection is not lost.
A question about a possible relationship needs both characteristics.

A decision routine

Use this short routine before collecting information. First, say the question in your own words. Second, name the characteristic or characteristics needed to answer it. Third, decide whether the question is about one characteristic or a possible connection between two. Finally, check that each planned record will contain exactly the information needed.

For a question about one characteristic, record one value per case. For a question about a possible connection, record two values for each same case. If a question seems to need more than two characteristics, do not force it into this lesson’s one-or-two choice. Clarify or narrow the question so you can identify what it is asking.

It is also important not to collect a second characteristic without a reason. Extra information can distract from the question and may not help answer it. A good choice is the smallest set of characteristics that directly answers the stated question.

Name what each recorded value represents.
Ask whether the question is about one characteristic or a connection between two.
Keep paired values linked to the same case.
Collect only information needed for the question.

Worked example

One question about one characteristic

A class asks, “Which type of book do students most often choose for independent reading?” Choose one-variable or two-variable data, and name the variable.

Identify what the question asks
The question asks which type of book students choose most often. It does not ask whether book choice is connected to another characteristic.
Name the needed information
Record each student’s chosen book type. That is one characteristic, so one-variable data fit.

Answer: Choose one-variable data. The variable is book type chosen for independent reading.

Check: A list of different book types does not make this a two-variable question. Each student contributes one value for one characteristic.

Worked example

Two characteristics connected to the same person

A class asks, “Do students who spend more time practising piano tend to play more pieces from memory?” Choose the data type and name the characteristics to record.

Notice the comparison
The question asks whether practice time is connected to the number of pieces played from memory. One characteristic alone cannot answer it.
Keep each pair together
For each student, record practice time and number of pieces played from memory. Those two values must belong to the same student. This is two-variable data.

Answer: Choose two-variable data: practice time and number of pieces played from memory for each student.

Check: If the practice times and piece counts were recorded without showing which values belonged to each student, the pairing would be lost and the question could not be addressed properly.

Worked example

Read a hypothetical paired-data display

A teacher makes this hypothetical scatter plot to ask whether students’ daily reading time is connected to the number of pages they read. Each point is one hypothetical student. What two variables are shown, and why are two-variable data needed?

Hypothetical reading data

Each dot represents one hypothetical student; the values are paired by student.

Read the axes
The horizontal axis shows reading time in minutes per day. The vertical axis shows pages read per day. These are two different characteristics.
Connect each point to one student
Each dot gives both values for one student. The pairing lets the class consider whether the two characteristics may be connected, so two-variable data are needed.

Answer: The variables are daily reading time and pages read per day. Two-variable data are needed because the question asks about a possible connection between them.

Check: These hypothetical points illustrate what paired information can look like. They are not measured observations, and a display by itself does not show that one characteristic causes the other.

Common mistakes and how to avoid them

Calling data two-variable because one variable has many possible answers.

Correction: Count characteristics, not answer choices. One characteristic can have many values.

Recording two characteristics but not asking how they may be connected.

Correction: Check the question’s purpose. Two separate facts do not automatically make a meaningful two-variable question.

Writing down the two values separately and losing which person they belong to.

Correction: Keep each pair together for the same person, item, or event.

Assuming a plotted pattern proves that one characteristic causes another.

Correction: A display can show paired values and possible patterns. It does not, by itself, explain why they occur.

Lesson summary

Choose one-variable data when the question asks about one characteristic.
Choose two-variable data when the question asks about a possible connection between two characteristics.
For two-variable data, record both values for each same case and keep them paired.
Let the question guide what you collect.

Check your understanding

Question 1

A student council asks, “Which school lunch option do students choose most often?” What data fit?

One-variable data: lunch option chosen
Two-variable data: lunch option and student’s shoe size
Two-variable data: lunch option and student’s favourite book, even though no connection is asked
No data are needed

Show answer and explanation

One-variable data: lunch option chosen

The question asks about one characteristic: the lunch option chosen.

Question 2

A class asks, “Is there a connection between a plant’s height and the number of days it has been growing?” What should be recorded for each plant?

Its height only
Its number of days only
Its height and number of days, kept together for that plant
The height of one plant and the days for a different plant

Show answer and explanation

Its height and number of days, kept together for that plant

The question asks about a possible connection between two characteristics, so both values are needed for each same plant.

Question 3

A survey asks for each person’s favourite music style and favourite colour. It does not ask whether these are connected. What is the best conclusion?

It is automatically a two-variable question because two answers are collected.
It may be two separate one-variable questions; the purpose does not ask about a connection.
It is one variable because every person gives two answers.
It cannot collect data.

Show answer and explanation

It may be two separate one-variable questions; the purpose does not ask about a connection.

Two answers alone do not make a question about a relationship. The stated purpose is to find two separate preferences.

Key terms

Data: Information collected to answer a question.
Variable: A characteristic that is recorded and can have different values.
Value: One recorded answer for a variable, such as “bus” for travel method.
Paired data: Two values kept together because they come from the same person, item, or event.
Scatter plot: A graph that uses dots to show pairs of numerical values.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 8 Mathematics, expectation D1.1. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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