D1. Data Literacy
Specific Expectations
Data Collection and Organization
D1.1
describe the difference between qualitative and quantitative data, and describe situations where each would be used
- questions of interest that require qualitative data to answer:
- What is the favourite type of book read in class? (e.g., fiction, non-fiction, graphic novel)
- What things do you do to protect the environment? (e.g., borrow or purchase second-hand items where possible, reduce food waste, recycle, turn off lights and devices when not in use)
- What kinds of programs does your community centre offer? (e.g., baseball, soccer, lacrosse, painting, photography, coding, cooking)
- questions of interest that require quantitative data to answer:
- Do birds prefer visiting the bird feeder in the morning or the afternoon?
- How far can Grade 4 students jump?
- How many blocks can a Grade 4 student stack in 30 seconds?
- It is important to know whether the data that is needed to answer a question is qualitative or quantitative, so that appropriate collection can be planned and carried out, appropriate representations chosen, and appropriate analysis conducted.
- Qualitative data involves variables that can be placed into categories, like “type of sports” or “colour”.
- Quantitative data involves variables that can be counted or ordered, like “the number of legs on an insect” or “the length of an object”.
Provide students with different questions of interest, and have them identify whether qualitative or quantitative data is needed to answer each question.
When students are creating their own questions of interest, have them identify whether the data they need to collect is qualitative or quantitative and explain why.
D1.2
collect data from different primary and secondary sources to answer questions of interest that involve comparing two or more sets of data, and organize the data in frequency tables and stem-and-leaf plots
- questions of interest:
- Which of the junior grades has the highest number of students who speak more than one language?
- How many trees are planted in Ontario each year?
- collection of data from different sources:
- primary data collection (e.g., observations, experiments, interviews, written questionnaires)
- secondary data collection (e.g., print media, online searches, Statistics Canada website)
- stem-and-leaf plot:
- The type and amount of data to be collected is based on the question of interest. Data can be either qualitative or quantitative. Sometimes more than one data set is needed to answer a question of interest.
- Data may need to be collected from a primary source through observations, experiments, interviews, or written questionnaires, or from a secondary source that has already collected the data, such as Statistics Canada or the school registry.
- Two or more data sets can be organized in separate frequency tables or within the same frequency table.
- A stem-and-leaf plot is one way to organize quantitative data. It can provide a sense of the shape of the data. The digits in the number are separated out into a stem and a leaf. For example, the number 30 has a stem of 3 and a leaf of 0. The stems and the leaves are ordered from least to greatest value in the plot.
Have students collect one piece of information from different populations and compare the results. For example, students might be interested in knowing how many students in each grade speak one language, and how many speak more than one. Have them organize the data in a frequency table like the following:
Have students collect and organize data on a question of interest that requires them to use secondary sources and make comparisons. For example, how many trees are planted in Ontario each year? Once students become comfortable working with these types of questions, have them gather data for multiple comparisons, such as the number of trees planted for a biodiversity project. Have students organize the data in a frequency table with multiple columns.
Have students organize the following list of data values using a stem-and-leaf plot. The data values represent the number of minutes that students read on a single night.
Data collected: 10, 15, 5, 35, 20, 10, 5, 20, 35, 35, 30, 10, 15, 15, 25, 15, 25
Data Visualization
D1.3
select from among a variety of graphs, including multiple-bar graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs
- types of graphs:
- pictograph
- line plot
- bar graph
- multiple-bar graph
- multiple-bar graphs:
- The graphs below show the daily physical activity levels of students in Grade 4 and Grade 5 in comparison to the Canadian Physical Activity Guidelines.
- Multiple-bar graphs show comparisons. They have bars in which data sets are shown side by side to compare two aspects of the data.
- Multiple-bar graphs can be created in more than one way, including with horizontal and vertical bars.
- The source, titles, labels, and scales provide important information about the data in a graph or table:
- The source indicates where the data was collected.
- The title introduces the data shown in the graph or table.
- Labels provide additional information, such as the labels on the axes of a graph describing what is being measured (the variable).
- Scales are indicated on the axis of bar graphs, showing frequencies, and in the key of pictographs.
Note
- The numerical values of the frequencies need to be considered when a scale is chosen.
- Depending on the scale that is chosen, the length of the bars on a bar graph may need to be estimated.
Provide students with two sets of stem-and-leaf plots displaying the number of minutes that students in Grades 4, 5, and 6 have read on Saturday and Sunday. Have them create a multiple-bar graph that shows the Grade 4, 5, and 6 data (total number of minutes) for Saturday, side by side, and the Grade 4, 5, and 6 data (total number of minutes) for Sunday, side by side.
Then have them create a second multiple-bar graph that shows the total number of minutes side by side for each grade, i.e., the Saturday and Sunday data for Grade 4 would be side by side, the Saturday and Sunday data for Grade 5 would be side by side, and the Saturday and Sunday data for Grade 6 would be side by side. Discuss how the two graphs show different information about the data.
Have students collect and display data about the favourite subjects of students in Grades 4, 5, and 6. Have them represent the data in a frequency table and in a variety of graphs, including multiple-bar graphs. Experiences like this help students develop critical-thinking skills as they decide what they want their graph to reveal about the data.
D1.4
create an infographic about a data set, representing the data in appropriate ways, including in frequency tables, stem-and-leaf plots, and multiple-bar graphs, and incorporating any other relevant information that helps to tell a story about the data
- infographic on the topic of “Junior Read-A-Thon”:
- Infographics are used to share data and information on a topic in an appealing way.
- Infographics contain different representations of the data, such as tables, plots, and graphs, and minimal text.
- Information to be included in an infographic needs to be carefully considered so that it is clear and concise.
- Infographics tell a story about the data with a specific audience in mind.
Note
- Creating infographics has applications in other subject areas, such as communicating key findings and messages in STEM projects.
To deepen students' understanding of what an infographic is and what it is used for, provide them with an infographic that has already been created, such as the “Junior Read-A-Thon” infographic found in the examples for D1.4. Ask questions to support their analysis. For example, ask what audience they think the infographic was intended for, or what messages they think the writer was trying to share.
Have students collect other infographics and, as a class, make a list of the features they see in the infographics. Discuss how these features can change depending on the audience and what story is being told about the data.
Have students create a story about the data they collected for a question of interest, for example, ways to support waste reduction through the school. Have them identify the audience they want to share their story with and what visuals and other key pieces of information they want to use to tell their story.
Data Analysis
The following is a list of responses from nine students to the question “How many cousins do you have?”: 24, 16, 30, 0, 14, 35, 14, 8, 3
- mode: 14
- Two of the responses were 14, which is more frequent than any other response.
- median: 14
Step 1: Rearrange the numbers in order from least to greatest.
- 0, 3, 8, 14, 14, 16, 24, 30, 35
Step 2: Identify the number in the middle.
- The median is 14.
- mean: 16
Step 1: Add all the numbers:
- 24 + 16 + 30 + 0 + 14 + 35 + 14 + 8 + 3 = 144
Step 2: Divide the sum by the number of values:
- 144 ÷ 9 = 16
- The mean is 16.
- The mean, median, and mode can be determined for quantitative data. Only the mode can be determined for qualitative data.
- The mean is calculated by adding up all of the values of a data set and then dividing that sum by the number of values in the set.
- The median is the middle data value for an ordered list. If there is an even number of data values, then the median is the mean of the two middle values in the ordered list.
- A variable can have one mode, multiple modes, or no mode.
Note
- The mean, median, and mode are the three measures of central tendency.
Provide data sets with a median that is easy to calculate – such as a set with 16 and 18 as middle numbers, so students can see that 17 is exactly halfway between them. For example:
Here is a stem-and-leaf plot showing the responses from eight students to the question “How many minutes have you pledged to read each day during the Read-A-Thon?”
- Modes: 15 and 20
- 15 minutes and 20 minutes are the most frequent numbers of minutes that students pledged to read each day during the Read-A-Thon.
- Median: 17 (mean of the two middle numbers, 16 and 18)
- Half the students pledged to read for more than 17 minutes each day during the Read-A-Thon, and the other half pledged to read for less than 17 minutes.
- Mean: 18
- 10 + 15 + 15 + 16 + 18 + 20 + 20 + 30 = 144
- 144 ÷ 8 = 18
- On average, students pledged to read for 18 minutes each day during the Read-A-Thon.
Have students determine the mean, median, and mode for data collected from a variety of sources for a variety of purposes. Purposes could include cross-curricular applications such as science experiments.
D1.6
analyse different sets of data presented in various ways, including in stem-and-leaf plots and multiple-bar graphs, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions
- various ways of presenting data:
- Different representations are used for different purposes to convey different types of information.
- Stem-and-leaf plots are helpful for quickly determining highest and lowest values, as well as the mode and median for a set of data.
- Multiple-bar graphs are used to organize data sets side by side and allow for easy comparisons between the sets of data.
- Data presented in tables, plots, and graphs can be used to ask and answer questions, draw conclusions, and make convincing arguments and informed decisions.
- Questions of interest are intended to be answered through the analysis of the representations. Sometimes the analysis raises more questions that require further collection, representation, and analysis of data.
Note
- There are three levels of graph comprehension that students should learn about and practise:
- Level 1: information is read directly from the graph and no interpretation is required.
- Level 2: information is read and used to compare (e.g., greatest, least) or perform operations (e.g., addition, subtraction).
- Level 3: information is read and used to make inferences about the data using background knowledge of the topic.
- As graphs become more sophisticated, have students highlight the parts of the graph they need to answer a question, including the scales when appropriate.
Provide students with a stem-and-leaf plot, a pictograph, a bar graph, or a multiple-bar graph, and ask them what questions they have about the data. Model the act of posing questions to support students in posing their own questions. For example (using the graphs below):
- question that requires reading and interpreting data from a graph or table:
- How many students in Grade 4 and in Grade 5 are getting the recommended level of daily physical activity?
- question that requires finding data from a graph or table and using it in a calculation:
- What is the difference in the number of students in Grade 4 and in Grade 5 who do the daily or more than the daily recommended level of physical activity?
- question that requires using data from a graph to make an inference or prediction:
- Why do you think that students in Grade 5 are more active than students in Grade 4?
Throughout the year, have students collect a variety of representations of real-life data about topics that interest them. Model asking questions using the three types of questions outlined in Task 1, and have students pose and answer their own questions, requiring them to think critically about the data.
