DoAssignment study guide
D1.2 · Collect and tabulate continuous two-variable data
Learn to collect and tabulate continuous two-variable data through clear examples and targeted practice.
Ontario Grade 8 Mathematics
Data
A Grade 8 lesson for expectation D1.2
Suppose a class wants to see how a plant’s height changes as it grows. Each time the class measures the plant, it records both the plant’s age and its height. These are two variables: quantities that can change. Since age and height can include decimal values, they are continuous data. In this lesson, you will learn how to collect such paired measurements, organize them clearly, and plot them without changing or inventing the observations.
What you will learn
- Identify two variables that can be measured and can take values between whole numbers.
- Collect paired measurements using a clear, consistent method.
- Organize paired measurements in a table and represent them on a labelled scatter plot.
1. Recognize continuous two-variable data
A variable is a quantity that can change. A measurement such as length, time, temperature, or mass is often continuous. Continuous data can take values between whole numbers. For example, a measured height might be cm or cm, depending on the measuring tool.
Two-variable data means that two measurements are recorded together for the same item or event. For a plant, one measurement could be its age in days and the other its height in centimetres. Each pair belongs to one measurement time. Keeping the pair together matters: an age must stay matched with the height measured at that age.
Before collecting data, decide what the two variables are, choose units, and use a consistent method. For example, measure the same plant from the soil surface to the top of its stem each time. Record the actual readings, including reasonable decimal places shown by the measuring tool. Do not fill gaps by guessing.
- A variable is a quantity that can change.
- Continuous data can include values between whole numbers.
- Two-variable data records a matched pair of measurements for each observation.
- Use clear units and the same measurement method each time.
2. Tabulate the paired measurements
A table is an organized way to display information in rows and columns. For two-variable data, use one column for each variable. Put the variable name and its unit in each column heading. Each row should contain the two measurements that belong together.
For example, imagine a class records a plant’s age and height. The following values are explicitly hypothetical practice data, not observations from a real plant. The row for day 4 shows that the plant was 2.8 cm tall when it was measured on that day.
A useful table preserves the original measurements. Do not sort one column on its own, because that could separate values that belong together. Check that every row has one age and one matching height, and that the headings make the units clear.
(age in days,height in cm)
- Use a heading for each variable, including its unit.
- Put each matched pair in the same row.
- Keep the original pairs together when organizing the data.
3. Plot and read the data carefully
A scatter plot is a graph that shows paired numerical data as separate points. Choose one variable for the horizontal axis and the other for the vertical axis. Label each axis with the variable and its unit. Choose a scale that includes every recorded value and spaces the points clearly.
To plot a pair, find its first measurement along the horizontal axis and its second measurement along the vertical axis. Place one point where those two positions meet. For example, the pair is plotted at age 4 days and height 2.8 cm. The point represents one recorded observation, not a prediction.
A graph makes it easier to see how the paired measurements are arranged. It does not change the data. A plot alone also does not explain why measurements have particular values. Stay with what the collected pairs show, and do not claim a cause just because two measurements appear to change together.
- A scatter plot uses one point for each paired observation.
- Label both axes and include units.
- Plot the first value horizontally and the second vertically.
- Represent the recorded data accurately; do not add unmeasured points.
Worked example
Example 1: Prepare a data table
A class takes hypothetical practice measurements of a plant. Its age is recorded in days and its height in centimetres. Organize the pairs , , , and in a table with clear headings.
- Name the measurementsThe first number in every pair is the plant’s age in days. The second is its height in centimetres. Use those names and units as the column headings.
- Keep each pair on one rowEach row records one measurement time and the matching height. Keeping the values together preserves the meaning of every observation.
Answer: | Age (days) | Height (cm) |
|---:|---:|
| 2 | 1.6 |
| 4 | 2.8 |
| 6 | 3.1 |
| 8 | 4.5 |
|---:|---:|
| 2 | 1.6 |
| 4 | 2.8 |
| 6 | 3.1 |
| 8 | 4.5 |
Check: There are four rows for four pairs, and every row keeps the age matched with its recorded height.
Worked example
Example 2: Plot paired measurements
Use the hypothetical plant data from Example 1. Identify the axes and explain how to plot the pair .
Each point shows one hypothetical practice measurement. Horizontal axis: age in days. Vertical axis: height in centimetres. The points are the four paired values from Example 1.
- Assign the axesPut age in days on the horizontal axis and height in centimetres on the vertical axis. These labels tell the reader what each position measures.
- Locate the pairMove to 6 days along the horizontal axis, then to 3.1 cm along the vertical axis. Place one point where those positions meet. That point stands for the recorded pair.
Answer: Label the horizontal axis “Age (days)” and the vertical axis “Height (cm)”. Plot one point at age 6 days and height 3.1 cm.
Check: The first value is used on the horizontal axis, and the second value is used on the vertical axis.
Worked example
Example 3: Check a table and graph plan
A student records the hypothetical pairs , , and for time in minutes and water temperature in degrees Celsius. State the table headings, the axes, and the point for the second pair.
Three explicitly hypothetical practice pairs. Horizontal axis: time in minutes. Vertical axis: water temperature in degrees Celsius.
- Use the variable names and unitsThe first value is time, measured in minutes, and the second is temperature, measured in degrees Celsius. Use these as the two column headings.
- Match the graph axes to the tablePut time on the horizontal axis and temperature on the vertical axis. The second pair is plotted using 5 minutes and 7.8 degrees Celsius.
Answer: Table headings: Time (min) and Water temperature (°C). Graph axes: horizontal, Time (min); vertical, Water temperature (°C). Plot the second pair at 5 minutes and 7.8 °C.
Check: The second pair remains together: its first value is time and its second value is temperature.
Common mistakes and how to avoid them
Leaving units out of the table headings or graph axes.
Correction: Name each measurement and include its unit so readers know what the numbers mean.
Putting the first value on the vertical axis and the second on the horizontal axis without saying so.
Correction: Choose and label the axes first. Then use the same order for every pair.
Reordering one column but not the other.
Correction: Keep each matched pair in the same row so the measurements stay connected.
Adding a point that was not measured.
Correction: Plot only the collected pairs. Mark practice data as hypothetical when it is not real observation.
Lesson summary
- Continuous measurements can include values between whole numbers.
- Collect two-variable data as matched pairs using a consistent method and clear units.
- Tabulate the pairs with one column per variable and one row per observation.
- A labelled scatter plot shows each pair as one point, with the first variable on the horizontal axis and the second on the vertical axis.
Check your understanding
Question 1
A student records the pairs and , where the first value is time in minutes and the second is length in centimetres. Which point represents the second pair if time is on the horizontal axis?
Show answer and explanation
The second pair is time 4 minutes and length 6.1 cm. Time goes on the horizontal axis, so the plotted pair is .
Question 2
Which table heading best identifies a column containing measured temperature values?
- Number
- Temperature (°C)
- Observation
- Second value
Show answer and explanation
Temperature (°C)
A clear heading names the variable and gives its unit. “Temperature (°C)” does both.
Question 3
A measurement table has five paired observations. How many points should its scatter plot show?
- Four
- Five
- Ten
- It depends on the units
Show answer and explanation
Five
Each paired observation is shown by one point, so five pairs give five plotted points.
Key terms
- Variable
- A quantity that can change, such as time or height.
- Continuous data
- Measured data that can take values between whole numbers.
- Paired measurements
- Two measurements recorded together because they belong to the same observation.
- Table
- An arrangement of information in rows and columns.
- Scatter plot
- A graph that shows paired numerical data as separate points.
Continue through Grade 8 Math
View the complete Grade 8 Math Ontario Grade 8 Mathematics curriculum and lessons
- D1.1 · Choose one-variable or two-variable data for a question
- D1.3 · Choose and label suitable graphs including scatter plots
- D1.4 · Create a data infographic with appropriate representations
- D1.5 · Describe strength and direction of two-variable relationships
- D1.6 · Critique scatter plots and misleading graphs before drawing conclusions
- D2.1 · Solve probability problems using tree and Venn diagrams
About this lesson and its review
Published by DoAssignment. This reviewed lesson follows Ontario Grade 8 Mathematics, expectation D1.2. 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.