D1.1 Describe the difference between discrete and continuous data, and provide examples of each.
Activity 1: Recognition and Description of Data Types
Here are three data collection situations carried out at the Cité des Jeunes School. Determine the type of data associated with each situation and explain your choice.
Situation 1
Parents claim that the Cité des Jeunes School is too far for their children to walk to their home. The parents conducted a survey in an effort to convince the school board to add school buses, they conducted a survey to show that it takes too long for their children to walk to school. Here is the data collected:
Required Travel Time to School for Cité des Jeunes Students
| Time | Frequency |
|---|---|
| 0 to 9 mins | 48 |
| 10 to 19 mins | 71 |
| 20 to 29 mins | 144 |
| 30 to 39 mins | 175 |
| 40 mins or more | 102 |
I see that the data from the first survey represents the number of minutes students take to get to school. This is continuous quantitative data. I know that quantitative data can be measured or counted using natural numbers. I also know that continuous data can be specified, for example, minutes can become seconds, or one could even count in hours. That's why I believe it's continuous quantitative data.
Situation 2
Annick recorded the accessories worn by the 28 students in her class. Here are the results of Annick's observation in a frequency table:
Accessories Worn by the Students in the Class
| Accessories Worn | Frequency |
|---|---|
| Eyeglasses | 6 |
| Watch | 25 |
| Earrings | 13 |
| Chains | 16 |
| Rings | 10 |
I see that the data from Annick's observation is qualitative data that can be counted and organized into non-numerical categories (for example, types of pets and eye colour). Annick counted the accessories that the students in her class wear and recorded the data in a frequency table.
Situation 3
Grade 2 teachers helped their students identify different polygons by the number of sides they have. Students classified shapes according to this geometric property and recorded their results in the frequency table below:
Number of Polygon Sides
| Polygon | Number of Sides |
|---|---|
| Triangle | 3 |
| Square | 4 |
| Rhombus | 4 |
| Pentagon | 5 |
| Hexagon | 6 |
| Heptagon | 7 |
| Octagon | 8 |
I see that the data represents the number of sides of different polygons. The number of sides represents discrete quantitative data, because they can be counted using whole numbers.
Source: translated from En avant, les maths!, 6e année, CM, Données, p. 3-4.
Activity 2: Provide Examples of Discrete and Continuous Data
Present students with an illustration. Ask them questions of interest related to the image and whether they need discrete or continuous data to answer them. For example, how many liters of maple syrup are produced in Eastern Ontario? What is the price of a one-litre bottle of maple syrup at various sugar shacks in the region? How many trees are tapped each year at La Sucrerie sugar shack? How many sugar shacks are there in Northern Ontario compared to Southern Ontario? How many centimetres of snow have fallen in the month of February over the past ten years?
