Introduction
Statistical Questions is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with statistical questions.
What Is Statistical Questions?
Statistical Questions means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Statistical Questions
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Read the question in the box below: Is this a statistical question, and why or why not?
- A. No, because it asks about a team that has a fixed number of players.
- B. Yes, because it asks about many different heights.
- C. No, because basketball teams always have the same average height.
- D. Yes, because you must collect data from many players whose heights vary.
Why it works: This is statistical because team members have different heights and you must collect data from multiple sources. The number of people or a team's fixed size does not prevent variability—different players still have different heights.
Answer: Yes, because you must collect data from many players whose heights vary.
Visual Model 2
Question: A researcher asks sixth graders: "How many hours do you sleep per night?" The table shows some responses: What does the variability in these responses tell us about the question?
| Student | A | B | C | D | E |
|---|---|---|---|---|---|
| Hours of Sleep | 8 | 9.5 | 7 | 8.5 | 9 |
- A. The question has no correct answer.
- B. The question is statistical because answers vary.
- C. All students should sleep the same amount.
- D. The question is not statistical.
Why it works: Variability in responses is a key indicator that a question is statistical. Different students sleep different amounts, which is expected and shows the question requires data collection to analyze.
Answer: The question is statistical because answers vary.
Worked Examples
Example 1
Question: A restaurant manager asks customers: "How much time did you spend eating lunch today?" Here are responses (in minutes): What does this data show about the question?
| 25 | 45 | 30 | 50 | 35 |
|---|
- A. The question is non-statistical.
- B. Everyone spends the same time eating lunch.
- C. The question is statistical because responses vary.
- D. Lunch time is always 30 minutes.
- The different responses (25, 45, 30, 50, 35 minutes) demonstrate that this question has variability and requires data collection, which are hallmarks of a statistical question.
Answer: The question is statistical because responses vary.
Example 2
Question: Consider these two questions: Which statement is correct?
| Question A | Question B |
|---|---|
| What is the weight of my dog? | What are the weights of dogs in my neighborhood? |
- A. Both are statistical.
- B. Question A is statistical; Question B is not.
- C. Question A is non-statistical; Question B is statistical.
- D. Neither is statistical.
- Question A asks about one dog (one answer).
- Question B asks about multiple dogs, whose weights vary, requiring data collection—making it statistical.
Answer: Question A is non-statistical; Question B is statistical.
Example 3
Question: A survey asks: "How many minutes do you exercise each day?" Five responses are shown: What does the range of responses (15 to 45 minutes) tell us?
| 15 | 30 | 20 | 45 | 25 |
|---|
- A. Everyone should exercise 30 minutes.
- B. The question is non-statistical.
- C. The question expects variability in answers, confirming it is statistical.
- D. There is an error in the data.
- The different responses show that people exercise different amounts.
- This variability is expected and indicates the question is statistical.
- Variability is a defining feature of statistical questions.
Answer: The question expects variability in answers, confirming it is statistical.
Real-World Word Problems
Problem 1
Question: A student rewrites a non-statistical question to make it statistical. Which is the BEST rewrite? Original: "How old is my teacher?"
- A. How old are the teachers at our school?
- B. In what year was my teacher born?
- C. How many teachers are there?
- D. What is the average age of all teachers in the United States?
Why it works: Rewriting "How old is my teacher?" to "How old are the teachers at our school?" introduces variability (different teachers have different ages) and requires collecting multiple data points. Options B, C, and D don't improve the statistical nature of the original question.
Answer: How old are the teachers at our school?
Problem 2
Question: A survey asks: "How many hours did you spend reading last week?" What is the population for this question?
- A. All the people whose reading time is being studied
- B. Hours of the day
- C. Books in the library
- D. The number 7
Why it works: The population is the entire group of people you want to learn about. In this survey, that group consists of all people whose reading hours the question targets (which could be all students in a class, all sixth graders, etc.).
Answer: All the people whose reading time is being studied
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Which of these is a statistical question?
- A. How tall am I?
- B. What is the capital of Texas?
- C. How many minutes do students in my class spend on homework each night?
- D. How many days are in a year?
Question 2
Which question is NOT statistical?
- A. What was the temperature each day last week?
- B. How many hours do sixth graders sleep each night?
- C. What is the favorite sport of students in this school?
- D. What is the boiling point of water?
Question 3
Which statement BEST describes a statistical question?
- A. It has a single, definite answer.
- B. It involves a very large number of people.
- C. It is asked only once per year.
- D. It anticipates variability and is answered by collecting data.
Question 4
A student asks: "How many hours per week do students in my grade spend exercising?" Why is this a statistical question?
- A. Because exercise is healthy.
- B. Because it involves numbers and hours.
- C. Because different students exercise different amounts, requiring data from many people.
- D. Because the question is asked in science class.
Question 5
A researcher asks students: "How many minutes did you exercise yesterday?" Which describes the population being sampled?
- A. All students in the school
- B. The number of minutes in a day
- C. The students who answered the survey
- D. All sixth graders in the state
Question 6
Which question would produce the MOST variability in answers?
- A. What time does lunch start at your school?
- B. How many legs do dogs have?
- C. What year was the Statue of Liberty built?
- D. How many siblings do you have?
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: How many minutes do students in my class spend on homework each night?
A statistical question anticipates variability and is answered by collecting data. Homework time varies across students, so that question is statistical; the others have a single fixed answer.
Question 2
Answer: What is the boiling point of water?
The boiling point of water has one fixed answer (100°C at sea level). The other questions all involve variability and require collecting data from multiple sources, making them statistical.
Question 3
Answer: It anticipates variability and is answered by collecting data.
By definition, a statistical question expects different answers from different sources and requires collecting and analyzing data. The size of the number or frequency of asking does not define a statistical question.
Question 4
Answer: Because different students exercise different amounts, requiring data from many people.
Variability (different exercise times) and multiple data sources (many students) are what make it statistical. Context (class, subject) and topic alone do not define a statistical question.
Question 5
Answer: All students in the school
If this survey asks all students in the school, that is the population. The sample would be the subset of students who actually answered the survey. Option C describes the sample, not the population.
Question 6
Answer: How many siblings do you have?
This question would produce the most variability: different students have different numbers of siblings (0, 1, 2, 3, etc.). The other questions have fixed or nearly-fixed answers across a group.
Connection to Standards
This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Statistical Questions becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
