D1.2 Collect continuous data to answer questions of interest involving two variables, and organize the data sets as appropriate in a table of values.
Activity 1: Organize a Data Set in a Table of Values
The management of the Adventure Baseball League wants to measure the speed of the ball thrown by the pitchers of the various teams. They want to determine if there is a relationship between the age of the player and the speed of the ball thrown.
Here is the table of values created by the league leaders.
| Age of Pitchers | Speed of the Thrown Ball (km/h) |
|---|---|
| 6 | 30.9 |
| 6 | 29.6 |
| 6 | 31.3 |
| 6 | 34.2 |
| 7 | 39.2 |
| 7 | 40.1 |
| 7 | 41.8 |
| 7 | 45.9 |
| 8 | 49.5 |
| 8 | 52.2 |
| 8 | 55.4 |
| 8 | 58.5 |
| 9 | 60.8 |
| 9 | 63.1 |
| 9 | 64.8 |
| 9 | 69.2 |
| 10 | 71.8 |
| 10 | 73.2 |
| 11 | 73.6 |
| 11 | 74.5 |
| 10 | 75.1 |
| 11 | 75.3 |
| 11 | 76.8 |
| 10 | 78.2 |
| 12 | 80.9 |
| 12 | 81.9 |
| 12 | 82.3 |
| 12 | 83.1 |
| 13 | 83.9 |
| 14 | 84.2 |
| 13 | 84.5 |
| 15 | 85 |
| 13 | 85.6 |
| 13 | 86.1 |
| 14 | 86.7 |
| 15 | 86.7 |
| 15 | 87.2 |
| 14 | 87.3 |
| 15 | 88.3 |
| 16 | 88.3 |
| 16 | 89.3 |
| 14 | 89.4 |
| 16 | 89.7 |
| 16 | 90 |
| 16 | 90.2 |
Allow time for students to analyse the table of values. Analysis can be done individually or in small groups. Teachers should then ask open-ended questions to help students communicate their observations and ideas in their own words and develop ideas from those of their peers. For example, they might ask:
- When you analyze this table of values, what do you notice?
- Do you think there is another way this table of values can be organized? How?
- What type of data are you analyzing? Is it primary or secondary? discrete or continuous? single-variable or two-variable? How do you know?
Have students create a new table of values based on their suggestions.
Activity 2: Two-Variable Data Sets
Choose one of the questions below and then collect the data needed to answer the question. Organize the data in a table of values, then explain whether the data used is primary or secondary data.
Sample questions to ask students include:
- Is the average height of 12-year-old students smaller than the height of 13-year-old students?
- Is there a relationship between the perimeter of a square and the length of its sides?
Source: translated from En avant, les maths!, 8e année, ML, Données, p. 4.