Minds On
Gathering data
There can be a lot of data to gather, record, and analyze when exploring a topic of interest. For example, what kind of data could you collect about a team or club in your community?
Create a question that can be answered by analyzing the following list of data display types. Record each question and your answer to it using a method of your choice.
1. Bar Graph
(Example: When is your preferred time to meet for practice? Options: early morning, during the day, in the evening).
2. Histogram
3. Table of values
Brainstorm
Two-variable data
Only one of the graphs you accessed previously includes two-variable data. Which one could it be? Why?
Throughout this learning activity, you can record your ideas digitally, orally, or in print.
Action
Task 1: One-variable or two-variable data
Do you know the difference between one-variable data and two-variable data?
A variable is any attribute, number, or quantity that can be measured or counted in various situations.
One-variable data is a measure of ONE fact or attribute from a sample or population. You will recognize one-variable situations when you identify:
- tally charts
- frequency tables
- bar graphs
- histograms
- pictographs
- circle graphs
One-variable data can be analyzed using mean, median, mode.
Two-variable data is a measure of TWO facts or attributes from the same sample or population. To compare the attributes, we use:
- ordered pairs (x, y)
- scatter plots
- two-column table of values
We analyze two-variable data to see if there is any relationship between the two variables.
Can you determine which data would be one-or-two variable data in these situations? For each situation, select the corresponding data.
One-or-two variable data situations
Choose one of the following three situations that includes either one-variable or two-variable data. Record your responses in a method of your choice.
1. Determine whether it is an example of one-or-two variable data
2. Provide an explanation for your answer.
Situation 1:
- The teacher calculates the median mark of the class on the Math test.
Situation 2:
- Across Ontario, the mosquito population remained low due to the lower-than-average rainfall.
Situation 3:
- A classroom survey shows that 70% of students plan to go into the field of Business, 15% plan to go into Medicine, 10% are going into the Trades, and 5% are uncertain.
Press ‘Answer’ to reveal the solutions.
Situation 1:
- One-variable data because you are only analyzing one fact about the data set. The information could have been recorded as a list or in a table.
Situation 2:
- Two-variable data because the population changes but so does the rainfall and you would try to find a relationship between the two. I would plot the data on a scatter plot.
Situation 3:
- One-variable data because we are only exploring what students are planning to study. It can be counted and I would plot the data on a circle graph or a bar graph.
One-or-two variable data in graphs
Choose two examples below that display either one-variable or two-variable data. Record your responses to the following in a method of your choice:
1. Determine whether it is an example of one-or-two variable data.
2. Provide an explanation for your answer.
Example 1:
Example 2:
The scatter plot shows pant measurements with the waist on the x-axis and the in-seam on the y-axis. The points represented are (25, 24), (27, 28), (27, 28), (30, 32.5), (33, 30), (34, 28), (35, 33). The first value in each coordinate pair indicates the waist in inches, and the second value indicates the in-seam in inches.
Example 3:
Press ‘Answer’ to reveal the solutions.
Example 1:
- one-variable data- only snowfall amount is being measured.
Example 2:
- pant measurements- two-variable data because the scatter plot is recording the relationship between the measurement of the inseam and the waist.
Example 3:
- one-variable because frequency of absences is the only thing being measured/counted.
Task 2: Identify the two variables
Analyze the following situations and answer the questions.
The following table displays the average electricity consumption.
- What are the two variables here being measured?
- How do you know that this is a two-variable situation?
|
Number of people in household |
Average electricity consumption per month (kWh) |
|---|---|
|
5 |
1,152 |
|
4 |
928 |
|
5 |
953 |
|
6 |
1,067 |
|
3 |
893 |
A teacher surveyed their students about how long they studied for their test.
- Which of the following two graphs display two-variable data? How do you know? What are the two variables?
Task 3: What type of graph should be created?
Analyze the following table:
|
Time Spent Playing Outside |
||
|---|---|---|
|
Students |
Hours During the Week |
Hours During the Weekend |
|
Child 1 |
2 |
2 |
|
Child 2 |
4 |
2 |
|
Child 3 |
1 |
6 |
|
Child 4 |
1 |
3 |
|
Child 5 |
3 |
4 |
Brainstorm
What graph would you choose?
What type of graph would be best to record a potential relationship between weekday outdoor play and weekend outdoor play? Explain your answer.
If possible, share your thinking with a partner.
Time to do the graph!
Create the graph about weekday outdoor play and weekend outdoor play using the Interactive Mathify Whiteboard or a method of your choice.
Press the ‘TVO Mathify’ button to access this resource and the ‘Activity’ button for your note-taking document.
TVO Mathify (Opens in new window) Activity (Open PDF in a new window)Consolidation
What are your responses?
Choose either Task 1 or Task 2 and record your responses using a method of your choice.
Task 1: One variable or two-variable data?
Suppose Learners A and B recorded the height measurements of the members of their household. Both learners decided to work together and create a scatter plot with the variable of height measurements they gathered to determine if there is a relationship between them.
- Why is the data collected not two-variable data?
- How could you change the data that was gathered to accurately graph this relationship in the data?
Task 2: Analyzing data in a variety of ways
Let’s explore the amount of time a variety of children spend on their interests each week.
Press the ‘Activity’ button to access Hours Spent On Their Interests.
- If you calculated the mean number of hours spent by a child each day on their interests, is this one-variable or two-variable data?
Reflect
Think of some situations where you would need to collect, analyze, and graph two-variable data. Record your thinking using a method of your choice.
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel…
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.
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 new window)