Mathematics · Grade 6 · Data, Statistics, and Variability · Term 4

Statistical Questions and Data Collection

Identifying questions that anticipate variability and understanding methods of data collection.

• Ontario Curriculum Expectations
• 6.SP.A.1

About This Topic

Statistical questions and variability introduce students to the world of data science. In Grade 6, students learn to distinguish between 'statistical questions' (which expect a variety of answers, like 'How much do my classmates' backpacks weigh?') and 'non-statistical questions' (which have one answer, like 'How much does my backpack weigh?'). They explore how data is distributed and why 'spread' matters as much as the 'middle.'

This topic is the foundation for critical thinking in a data-driven world. It teaches students to look for patterns and outliers and to understand that 'average' doesn't tell the whole story. This topic comes alive when students can physically model the patterns by collecting their own data from the class and physically arranging themselves to show the distribution.

Key Questions

1. Differentiate between a statistical question and a non-statistical question.
2. Explain how variability in a data set impacts the conclusions we can draw.
3. Design a statistical question and a plan for collecting relevant data.

Learning Objectives

• Classify questions as statistical or non-statistical based on whether they anticipate variability in their answers.
• Explain how the presence of variability in a data set influences the types of conclusions that can be drawn.
• Design a statistical question appropriate for a given context and outline a plan for collecting relevant data.
• Compare and contrast the characteristics of statistical and non-statistical questions.

Before You Start

Types of Data

Why: Students need a basic understanding of different types of data (e.g., numerical, categorical) to effectively plan data collection.

Asking Questions

Why: Students should have experience formulating questions, which is a foundational skill for designing statistical questions.

Key Vocabulary

Statistical Question	A question that anticipates and accounts for variability in the answers. For example, 'How many hours do Grade 6 students sleep each night?'
Non-Statistical Question	A question that has a single, predictable answer. For example, 'What is the capital of Ontario?'
Variability	The extent to which data points in a set differ from each other. It describes the spread or dispersion of the data.
Data Collection Plan	A detailed strategy for gathering information, including specifying the question, the population or sample, and the method of collection.

Watch Out for These Misconceptions

Common Misconception

Thinking that any question about a group is a statistical question.

What to Teach Instead

Clarify that a question like 'How many students are in this room?' is not statistical because there is only one answer. A statistical question must allow for a range of different responses from the individuals in the group.

Common Misconception

Believing that variability is a 'mistake' or a sign of bad data.

What to Teach Instead

Use examples like heights or shoe sizes. Explain that variability is a natural part of the world. Peer discussion about 'diversity' in data helps students see variability as information rather than an error.

Active Learning Ideas

Formal Debate: Is it Statistical?

Give students a list of questions. In small groups, they must categorize them as statistical or not and then debate their choices with another group, focusing on whether the question anticipates variability.

20 min·Small Groups

Inquiry Circle: The Variability Hunt

Groups choose a topic (e.g., height, number of siblings, commute time). They collect data from the class and create a simple dot plot to show the variability, discussing why the data isn't all the same.

35 min·Small Groups

Think-Pair-Share: The Story of the Spread

Show two dot plots with the same mean but different spreads. Students discuss in pairs: 'If these were test scores, which class would you rather be in and why?' then share their insights on variability.

15 min·Pairs

Real-World Connections

• Market researchers design statistical questions to understand consumer preferences for new products, like a new flavour of ice cream. They collect data through surveys to see the range of opinions and plan marketing strategies based on this variability.
• Public health officials use statistical questions to track the spread of illnesses in a community, such as 'How many students in this school have the flu this week?' They collect data from clinics and schools to understand the variability and inform public health interventions.

Assessment Ideas

Quick Check

Present students with a list of 5-6 questions. Ask them to label each question as either 'Statistical' or 'Non-Statistical' and provide a one-sentence justification for their choice.

Exit Ticket

Ask students to write one statistical question about their classmates and then outline a simple plan to collect the data. The plan should include who they would ask and how they would ask them.

Discussion Prompt

Pose the question: 'Why is it important to consider variability when asking questions about groups of people?' Facilitate a class discussion, guiding students to explain how variability affects the conclusions they can make.

Frequently Asked Questions

What makes a question 'statistical'?

A question is statistical if you expect to get a variety of different answers when you ask it. It's about looking for a pattern in a group rather than a single fact about one person or thing.

Why is variability important in Grade 6 math?

Variability tells us how consistent or diverse our data is. In the real world, knowing the 'spread' of data helps us make better predictions and understand risks, which is a key part of the Ontario Data Literacy expectations.

How can active learning help students understand variability?

Active learning strategies like 'The Variability Hunt' put students in charge of the data. When they collect and plot their own information, they see the variability firsthand. Discussing their own 'outliers' makes the concept of spread personal and memorable.

How can I use multicultural data to teach statistics?

Use data about the diverse languages spoken in Canadian homes or the different countries of origin for immigrants in your city. This allows students to explore variability within a context that reflects Canada's multicultural identity.