The mathematical purpose of this lesson is to understand what makes a question statistical and classify data as numerical or categorical. This unit begins with creating data displays and describing distributions of numerical data. Later in the course, students create and interpret two-way tables using categorical data. Numerical data are responses to questions that are numbers that can be ordered in a natural way. Categorical data are responses to questions that fit into distinct categories.
Students learn to recognize statistical questions as questions that anticipate variability in the data. In this lesson, students recall the concept of variability to discuss the difference between statistical and non-statistical questions while they collect survey data from their classmates. (The data will be used again in later lessons, so it should be kept in a spreadsheet or a folder.) Students classify questions as being statistical or non-statistical, and classify the data that they collect from statistical questions as numerical or categorical.
When students identify data resulting from a statistical question as numerical or categorical, students are engaging in MP2 because the are having to make sense of data in relation to the question being asked. Students also build from informal to more precise language, MP6, for several vocabulary terms that will be used throughout the unit.
- Describe (orally and in writing) the difference between statistical and non-statistical questions.
- Describe (orally and in writing) the distinctions between numerical and categorical data.
- Let's work together to collect data and explore statistical questions.
At the end of the Representing Data About You and Your Classmates activity, students will need to keep their data for use in a later lesson where students will represent the data collected in this activity graphically. If they record the data in workbooks, it will be easy to retrieve later. If students record data some other way, be sure your method allows them to easily retrieve the data later.
- I can tell statistical questions from non-statistical questions and can explain the difference.
- I can tell the difference between numerical and categorical data.
Categorical data are data where the values are categories. For example, the breeds of 10 different dogs are categorical data. Another example is the colors of 100 different flowers.
A non-statistical question is a question which can be answered by a specific measurement or procedure where no variability is anticipated, for example:
- How high is that building?
- If I run at 2 meters per second, how long will it take me to run 100 meters?
Numerical data, also called measurement or quantitative data, are data where the values are numbers, measurements, or quantities. For example, the weights of 10 different dogs are numerical data.
A statistical question is a question that can only be answered by using data and where we expect the data to have variability, for example:
- Who is the most popular musical artist at your school?
- When do students in your class typically eat dinner?
- Which classroom in your school has the most books?