Middle School Math Quiz: Recognize Statistical Questions
20 questions · exam conditions
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Recognize Statistical QuestionsQuestion 1 of 20

Mr. Rodriguez wants to collect data that will show variation in responses. He is deciding between these three questions for his survey. Which question would be LEAST likely to produce the variability he is looking for?

"How many hours per week do students in our school spend on homework?"
"What are the different heights of students in the sixth grade?"
"What is the exact distance from the school's front door to the flagpole?"
"How much money do students typically spend on lunch each day?"
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Middle School Math Quiz

Middle School Math Quiz: Recognize Statistical Questions

Practice Recognize Statistical Questions in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Recognize Statistical Questions, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Mr. Rodriguez wants to collect data that will show variation in responses. He is deciding between these three questions for his survey. Which question would be LEAST likely to produce the variability he is looking for?

  1. "How many hours per week do students in our school spend on homework?"
  2. "What are the different heights of students in the sixth grade?"
  3. "What is the exact distance from the school's front door to the flagpole?" (correct answer)
  4. "How much money do students typically spend on lunch each day?"
Explanation: The question about the distance from the school's front door to the flagpole has one fixed, measurable answer that will not vary regardless of who answers it. This makes it non-statistical. The other three questions all anticipate variability: homework hours will differ among students, student heights vary significantly, and lunch spending varies by individual choices and circumstances.

Question 2

A student council wants to ask questions that will help them make decisions based on data that shows student preferences and behaviors. They need to distinguish between questions that will give them useful variable data versus questions that will only give them fixed information. Which question would provide the LEAST useful data for understanding student variability?

  1. "What types of music do students in our school prefer for school dances?"
  2. "How much time do students spend on social media each day?"
  3. "What activities would students like to see added to our after-school program?"
  4. "What is the official start time for first period at our school?" (correct answer)
Explanation: When analyzing survey questions for data collection, you need to distinguish between questions that reveal variable data (information that changes from person to person) versus fixed information (facts that remain constant regardless of who answers). The correct answer is D because "What is the official start time for first period at our school?" asks for a fixed fact that never changes. Every student would give the exact same answer since there's only one official start time. This provides zero information about student variability or preferences – it's simply asking for a school policy that's already established. Let's examine why the other options are wrong: Choice A asks about music preferences, which will vary significantly among students – some might prefer pop, others rock, hip-hop, or country. Choice B asks about social media usage time, which will produce a wide range of responses from zero minutes to several hours daily. Choice C asks about desired after-school activities, where students will suggest different sports, clubs, or programs based on their individual interests. Notice that options A, B, and C all ask "what do you prefer/do/want" while option D asks "what is the official policy." The first type generates diverse responses that help understand the student body, while the second type simply confirms existing information. Strategy tip: When evaluating survey questions, ask yourself "Could different people reasonably give different answers to this question?" If everyone would give the identical response, it won't provide useful variable data for decision-making.

Question 3

A researcher is studying statistical thinking in students. She gives them four questions and asks them to identify which ones are statistical. The students must understand that statistical questions can be about individuals within a group, not just about groups as a whole. Which question tests this deeper understanding?

  1. "How old are the teachers at Lincoln Middle School?" - asking about ages across a group
  2. "How old is Mrs. Johnson?" - asking about one specific person's definite age
  3. "How old is a randomly selected student from the cafeteria?" - asking about one person's unknown age (correct answer)
  4. "What is the average age of students in sixth grade?" - asking for a calculated summary statistic
Explanation: This question tests the subtle understanding that statistical questions can ask about individuals when the specific individual is unknown or randomly selected, creating uncertainty and anticipated variability in the answer. Even though it asks about "a" student (singular), we don't know which student, so the age could vary. Choice A is clearly statistical (group variability). Choice B is clearly non-statistical (specific person, definite answer). Choice D, while involving statistics, asks for one calculated value rather than anticipating variability in responses.

Question 4

A market research company is designing survey questions for different purposes. Some questions are meant to gather statistical data that shows variation, while others are meant to gather specific factual information.

The research company needs to write questions that will generate statistical data for analysis. Which question would be MOST appropriate for this purpose because it best anticipates meaningful variability in responses?

  1. "What year was the iPhone first released to the public?"
  2. "How many smartphones do people in this city typically own?" (correct answer)
  3. "What is the current CEO of Apple's full name?"
  4. "What is the official price of the newest iPhone model?"
Explanation: "How many smartphones do people in this city typically own?" is statistical because it anticipates variability - different people will own different numbers of smartphones (0, 1, 2, or more), creating a data set that can be analyzed. The other three questions all have single, factual answers that do not vary: the iPhone release year is 2007, the CEO has one name, and there is one official price for the newest model.

Question 5

A teacher wants students to understand that the wording of a question can determine whether it's statistical or not, even when asking about the same general topic. Which pair of questions about test scores best illustrates this concept?

  1. "What was the highest score on yesterday's math test?" and "What scores did students earn on yesterday's math test?" (correct answer)
  2. "What was your score on the math test?" and "What was your score on the science test?"
  3. "How many students took the math test?" and "How many students took the science test?"
  4. "Who scored highest on the math test?" and "Who scored lowest on the math test?"
Explanation: This pair demonstrates how wording affects whether a question is statistical. "What was the highest score on yesterday's math test?" asks for one specific value (non-statistical), while "What scores did students earn on yesterday's math test?" anticipates multiple different values showing variability (statistical). Both questions are about the same test, but the wording changes whether variability is expected. The other choices either ask about different topics or contain questions that are both non-statistical.

Question 6

Rewrite the non-statistical question as a statistical question.

Non-statistical: "How many minutes did I practice piano yesterday?"

Which rewrite is statistical?​

  1. "How many minutes did I practice piano yesterday at 6:00 PM?"
  2. "How many minutes do students in my class practice piano on a typical day?" (correct answer)
  3. "How many minutes are in 1 hour?"
  4. "How many minutes did I practice piano yesterday, rounded to the nearest minute?"
Explanation: This question tests recognizing statistical questions as those anticipating variability in data (expect different answers from different subjects), vs non-statistical (single answer, no variability expected). Statistical questions anticipate data will vary (not all same answer), requires collecting multiple data points showing distribution; examples include 'How old are students in my school?' which expects variability (ages differ: some 11, some 12, some 13—data varies across students, statistical) and 'How many pets do students have?' which anticipates varying answers (0,1,2,3,... pets differ by student, statistical), while non-statistical have a single answer with no variability, like 'How old am I?' (one person, one age: 12, no variability—not statistical) or 'What is 5+3?' (one answer: 8, no data collection, not statistical), with variability being key since statistical questions are designed knowing answers will differ, accounting for variation in responses. For example, 'How tall are 6th graders?' is statistical (heights vary: 140 cm, 155 cm, 162 cm, 170 cm for different students, data distribution expected, anticipates variability), while 'How tall is the tallest 6th grader?' is not statistical (asks for one specific value: tallest is a single measurement like 170 cm, no variability—specific answer), and 'What is the average sleep hours?' is not statistical (average is one calculated value, even though based on varied data, the average itself doesn't vary—asking for single number). The rewrite in B is statistical because it expands to multiple students on a typical day, expecting varying practice times, while others remain focused on one instance or a fixed fact, so choice B is correct. A common error is thinking slight changes like adding a time or rounding make it statistical, but they still yield single answers without variability; another mistake is confusing math facts with data collection. To recognize statistical questions: (1) read the question carefully (what is being asked?), (2) consider the subjects (one person? or multiple people/trials?), (3) anticipate the answers (would answers vary? or single answer?), (4) classify (variability expected→statistical, single answer→not statistical). For instance, 'How many books did students read?' is statistical (varies by student: 2,5,8,12 books for different students, distribution expected), while 'How many books did I read?' is not (one person, one answer: 8 books, no variability); the key is variability in data, not just asking about multiple items—'What is the tallest player height?' asks about multiple players but wants one specific answer (tallest), so not statistical, and mistakes include confusing broad scope with variability (broad≠statistical if asking for single value) or thinking group questions are always statistical (specific within group can be single answer) without checking if variability is expected.

Question 7

Students are learning to identify statistical questions by considering whether the question anticipates variability. They encounter this question: "How long does it take students in our school to eat lunch?" A student argues this is NOT statistical because "lunch period is always 30 minutes." What is wrong with this reasoning?

  1. The student incorrectly assumed that time-based questions are never statistical in nature
  2. The student confused the lunch period duration with individual eating time variations (correct answer)
  3. The student failed to recognize that questions about groups are automatically statistical
  4. The student misunderstood that statistical questions must have exactly four possible answer choices
Explanation: When you encounter questions about statistical thinking, focus on whether the question anticipates variability in responses. A statistical question expects different answers from different individuals or observations. The question "How long does it take students in our school to eat lunch?" is definitely statistical because it asks about individual eating times, which will vary from student to student. Some students might finish their lunch in 10 minutes, others might take 25 minutes, and still others might fall somewhere in between. This variability in eating speeds makes it a statistical question. The correct answer is B because the student confused two completely different things: the lunch period duration (which is fixed at 30 minutes for everyone) with individual eating time variations (which differ from person to person). Just because the lunch period is always 30 minutes doesn't mean every student uses all 30 minutes to eat. Answer A is wrong because time-based questions can absolutely be statistical - this question proves it. Answer C is incorrect because not all questions about groups are automatically statistical; for example, "What is the name of our school?" is about a group but expects only one answer. Answer D is completely off-track since statistical questions have nothing to do with having exactly four answer choices. Study tip: When identifying statistical questions, ask yourself: "Would I expect different answers if I asked this question to multiple people or observed multiple cases?" If yes, it's statistical. Don't get distracted by fixed constraints like schedules or rules.

Question 8

A student wrote these questions for a class survey. Which questions are statistical questions (they expect answers to vary)?

  1. "How old are students in my school?"
  2. "How old am I?"
  3. "How many hours do 6th graders sleep on a school night?"
  4. "What is 5+35+3?"
  1. All four questions are statistical
  2. 2 and 4 only
  3. 1, 2, and 3 only
  4. 1 and 3 only (correct answer)
Explanation: A statistical question is one where you expect the answers to vary—different people or things might give different results. Let's test each question by asking, "Would the answers be the same every time, or would they change?" Question 1: "How old are students in my school?" Students have many different ages, so the answers vary. ✓ Statistical! Question 3: "How many hours do 6th graders sleep on a school night?" Different kids sleep different amounts, so the answers vary. ✓ Statistical! The other questions each have just one fixed answer that never changes, so they aren't statistical. That makes the answer D) 1 and 3 only. Think of it like this: "What color are everyone's shoes?" expects lots of different answers, but "What color are my shoes?" has just one. Variety means statistical! Try this at home: Make up two questions about your family—one with one answer, one with many!

Question 9

Rewrite the non-statistical question as a statistical question.

Non-statistical: "How tall am I?"

  1. "How tall are students in my class?" (correct answer)
  2. "What is my height to the nearest centimeter?"
  3. "Is my height greater than 150 cm?"
  4. "How tall is the tallest student in my class?"
Explanation: This question tests recognizing statistical questions as those anticipating variability in data (expect different answers from different subjects), vs non-statistical (single answer, no variability expected). Statistical questions anticipate data will vary (not all same answer), require collecting multiple data points showing distribution, like 'How old are students in my school?' with varying ages (11, 12, 13), or 'How many pets do students have?' expecting different numbers (0, 1, 2). For example, 'How tall are 6th graders?' is statistical due to height variability, but 'How tall is the tallest 6th grader?' is not (single value), and 'What is average sleep hours?' is not, as it's one calculated number. The best rewrite is A, changing the single 'am I' to group 'students' expecting varying heights, unlike B (single measurement), C (yes/no), or D (single tallest). A mistake is choosing D, confusing a specific group metric with variability, but it seeks one value. To rewrite, expand from one subject to multiple with anticipated differences. Key: focus on introducing variability through multiple subjects or instances.

Question 10

Compare the two questions:

A: "What is the weather today after school?"
B: "What is the weather after school each day this week (Monday through Friday)?"

Which statement is correct?

  1. Neither A nor B is statistical
  2. A is statistical and B is not statistical
  3. A is not statistical and B is statistical (correct answer)
  4. Both A and B are statistical
Explanation: This question tests recognizing statistical questions as those anticipating variability in data (expect different answers from different subjects), vs non-statistical (single answer, no variability expected). Statistical questions anticipate data will vary (not all same answer), requires collecting multiple data points showing distribution; examples include 'How old are students in my school?' which expects variability (ages differ: some 11, some 12, some 13—data varies across students, statistical) and 'How many pets do students have?' which anticipates varying answers (0,1,2,3,... pets differ by student, statistical), while non-statistical have a single answer with no variability, like 'How old am I?' (one person, one age: 12, no variability—not statistical) or 'What is 5+3?' (one answer: 8, no data collection, not statistical), with variability being key since statistical questions are designed knowing answers will differ, accounting for variation in responses. For example, 'How tall are 6th graders?' is statistical (heights vary: 140 cm, 155 cm, 162 cm, 170 cm for different students, data distribution expected, anticipates variability), while 'How tall is the tallest 6th grader?' is not statistical (asks for one specific value: tallest is a single measurement like 170 cm, no variability—specific answer), and 'What is the average sleep hours?' is not statistical (average is one calculated value, even though based on varied data, the average itself doesn't vary—asking for single number). Question A is not statistical as it asks for one day's weather (single answer), while B is statistical because weather varies across days, so A is not and B is, making choice C correct. A common error is calling broad questions like A statistical due to potential interpretations, but it specifies one time with no variability; another mistake is assuming questions about weather are always statistical without checking the scope for variation. To recognize statistical questions: (1) read the question carefully (what is being asked?), (2) consider the subjects (one person? or multiple people/trials?), (3) anticipate the answers (would answers vary? or single answer?), (4) classify (variability expected→statistical, single answer→not statistical). For instance, 'How many books did students read?' is statistical (varies by student: 2,5,8,12 books for different students, distribution expected), while 'How many books did I read?' is not (one person, one answer: 8 books, no variability); the key is variability in data, not just asking about multiple items—'What is the tallest player height?' asks about multiple players but wants one specific answer (tallest), so not statistical, and mistakes include confusing broad scope with variability (broad≠statistical if asking for single value) or thinking group questions are always statistical (specific within group can be single answer) without checking if variability is expected.

Question 11

Is the question "What is the weather today in our town?" a statistical question?

  1. Yes, because weather can change
  2. Yes, because it might rain later
  3. No, because it is asking about one day with one set of conditions (correct answer)
  4. No, because weather is not related to math
Explanation: This question tests recognizing statistical questions as those anticipating variability in data, meaning they expect different answers from different subjects, versus non-statistical questions that have a single answer with no variability expected. A statistical question anticipates that the data will vary, so it requires collecting multiple data points to show a distribution, such as 'How old are students in my school?' which expects ages to differ like 11, 12, or 13 across students, or 'How many pets do students have?' which anticipates varying numbers like 0, 1, 2, or 3 per student; non-statistical questions have one answer without variability, like 'How old am I?' which is just one age for one person, or 'What is 5+3?' which is always 8. For example, 'How tall are 6th graders?' is statistical because heights vary like 140 cm, 155 cm, or 170 cm among different students, creating an expected data distribution, while 'How tall is the tallest 6th grader?' is not statistical as it asks for one specific value like 170 cm without variability, and 'What is the average sleep hours?' is not statistical since the average is a single calculated number even if based on varied data. The question 'What is the weather today in our town?' is not statistical because it asks about one specific day with one set of conditions, expecting a single answer, so the correct answer is C. A common error is thinking weather questions are statistical due to potential changes, like claiming it varies throughout the day, but the question specifies 'today' as one instance without requiring multiple data points. To recognize statistical questions, read the question carefully to see what is being asked, consider if it involves multiple subjects or trials, anticipate if answers would vary across them, and classify based on whether variability is expected. Remember, the key is variability in the data, not just mentioning multiple items; questions about a single time or event are not statistical even if the topic can change over time.

Question 12

A teacher writes these questions on the board:

  1. "How many pets do students in our class have?"
  2. "How many pets does my best friend have?"
  3. "What is 12−512-5?"
  4. "How many minutes does it take students in our class to get to school?"

Which of the questions are statistical questions (they expect answers to vary)?

  1. 1, 2, and 4 only
  2. All four questions
  3. 2 and 3 only
  4. 1 and 4 only (correct answer)
Explanation: This question tests recognizing statistical questions as those anticipating variability in data, meaning they expect different answers from different subjects, versus non-statistical questions that have a single answer with no variability expected. A statistical question anticipates that the data will vary, so it requires collecting multiple data points to show a distribution, such as 'How old are students in my school?' which expects ages to differ like 11, 12, or 13 across students, or 'How many pets do students have?' which anticipates varying numbers like 0, 1, 2, or 3 per student; non-statistical questions have one answer without variability, like 'How old am I?' which is just one age for one person, or 'What is 5+3?' which is always 8. For example, 'How tall are 6th graders?' is statistical because heights vary like 140 cm, 155 cm, or 170 cm among different students, creating an expected data distribution, while 'How tall is the tallest 6th grader?' is not statistical as it asks for one specific value like 170 cm without variability, and 'What is the average sleep hours?' is not statistical since the average is a single calculated number even if based on varied data. In this case, questions 1 and 4 are statistical because they ask about pets and commute times for multiple students, expecting varied responses, while 2 is about one best friend with a single answer, and 3 is a math problem with one fixed result, so the correct answer is A: 1 and 4 only. A common error is thinking any question about a group is statistical, like claiming 2 is statistical because a best friend might have varying pets over time, but it asks for a single current number without expected variability, or misclassifying math questions as statistical if they involve numbers. To recognize statistical questions, read the question carefully to see what is being asked, consider if it involves multiple subjects or trials, anticipate if answers would vary across them, and classify based on whether variability is expected. Remember, the key is variability in the data, not just mentioning multiple items; for instance, 'What is the tallest player's height?' asks about multiple players but seeks one specific value, so it's not statistical, while questions about distributions like heights of all players are statistical.

Question 13

A student is designing a survey for her science project. She wants to investigate whether different types of questions will produce useful data for her analysis. Which pair of questions would allow her to compare a statistical question with a non-statistical question?

  1. "How many pets do students in our class have?" and "How many pets does Sarah have?" (correct answer)
  2. "What is your favorite color?" and "What is the most popular color among students?"
  3. "How tall are you?" and "How much do you weigh?"
  4. "What time does school start?" and "What time does school end?"
Explanation: A statistical question anticipates variability in responses. "How many pets do students in our class have?" expects different answers from different students (some may have 0, 1, 2, or more pets), making it statistical. "How many pets does Sarah have?" has only one specific answer, making it non-statistical. Choice B contains two statistical questions since both anticipate variability. Choice C contains two statistical questions since both height and weight vary among individuals. Choice D contains two non-statistical questions since both have fixed, single answers.

Question 14

Emma is analyzing whether questions from her class survey are statistical or non-statistical. She notices that one question received 25 identical responses from 25 different students. Based on this outcome, what can she conclude about whether this question was statistical?

  1. It was definitely a non-statistical question because all responses were the same
  2. It was definitely a statistical question because multiple people answered it
  3. It could still be a statistical question if it was designed to expect variability (correct answer)
  4. It cannot be determined without knowing how many students were surveyed total
Explanation: A question is statistical if it is designed to anticipate variability, regardless of whether the actual responses vary. For example, "What is your favorite subject?" is statistical even if all students happened to answer "math." The key is whether variability was expected when the question was written, not whether variability actually occurred in the responses. Choice A incorrectly focuses on the outcome rather than the question's design. Choice B incorrectly assumes multiple respondents make a question statistical. Choice D is irrelevant to determining if a question is statistical.

Question 15

Two questions are shown:

A) "What is the height of the tallest player on the basketball team?" B) "What are the heights of the players on the basketball team?"

How do these questions differ?

  1. Neither is statistical because height is a measurement
  2. A is statistical and B is not statistical
  3. Both are statistical because they are about a team
  4. A is not statistical and B is statistical (correct answer)
Explanation: This question tests recognizing statistical questions as those anticipating variability in data, meaning they expect different answers from different subjects, versus non-statistical questions that have a single answer with no variability expected. A statistical question anticipates that the data will vary, so it requires collecting multiple data points to show a distribution, such as 'How old are students in my school?' which expects ages to differ like 11, 12, or 13 across students, or 'How many pets do students have?' which anticipates varying numbers like 0, 1, 2, or 3 per student; non-statistical questions have one answer without variability, like 'How old am I?' which is just one age for one person, or 'What is 5+3?' which is always 8. For example, 'How tall are 6th graders?' is statistical because heights vary like 140 cm, 155 cm, or 170 cm among different students, creating an expected data distribution, while 'How tall is the tallest 6th grader?' is not statistical as it asks for one specific value like 170 cm without variability, and 'What is the average sleep hours?' is not statistical since the average is a single calculated number even if based on varied data. Question A is not statistical because it seeks the single height of the tallest player, while B is statistical as it asks for the varying heights of all players, so the correct answer is C. A common error is thinking both are non-statistical because they involve measurement, or both statistical because they are about a team, but the distinction is whether the question expects a distribution of varying data or one specific value. To recognize statistical questions, read the question carefully to see what is being asked, consider if it involves multiple subjects or trials, anticipate if answers would vary across them, and classify based on whether variability is expected. Remember, the key is variability in the data, not just mentioning multiple items; questions seeking extremes like tallest or maximum are not statistical, as they result in a single answer.

Question 16

Ms. Chen wants to help her students understand the difference between questions that produce data sets versus questions that produce single values. She writes several questions on the board. Which question would produce a data set with multiple values rather than just one answer?

  1. "What is the total number of books in our school library?"
  2. "What is the most common eye color among students in our class?"
  3. "What percentage of our class has brown eyes?"
  4. "What eye colors are represented among students in our class?" (correct answer)
Explanation: When you encounter questions about data collection, you need to distinguish between questions that yield a single answer versus those that produce multiple data points that can be analyzed. Question D asks "What eye colors are represented among students in our class?" This produces a data set because you'd collect individual responses from each student (brown, blue, green, hazel, etc.), creating multiple data points that could be organized, counted, and analyzed in various ways. Let's examine why the other options produce single values: Option A asks for "the total number of books in our school library" — this yields one specific number, not a collection of data points. Option B seeks "the most common eye color" — while you'd need to collect data to find this answer, the question itself asks for just one result (the mode of the data). Option C asks for "what percentage of our class has brown eyes" — again, this requires data collection but produces a single percentage as the final answer. The key difference is that option D asks for all the different eye colors present, which means you're looking for the range of values in your data set rather than calculating or identifying one specific result from that data. Remember this pattern: questions asking "what types," "what kinds," or "what varieties" typically produce data sets, while questions asking for totals, percentages, averages, or "most common" typically produce single calculated values.

Question 17

A science class asks these questions while doing a paper-airplane experiment:

  1. "How far did my airplane fly on one throw?"
  2. "How far do students' airplanes fly when each student throws once?"
  3. "How far do airplanes fly when the same airplane is thrown 10 times?"
  4. "What is 30÷530 \div 5?"

Which questions are statistical?

  1. 1, 2, 3, and 4
  2. 1 and 4 only
  3. 2 and 3 only (correct answer)
  4. 2 only
Explanation: This question tests recognizing statistical questions as those anticipating variability in data, meaning they expect different answers from different subjects, versus non-statistical questions that have a single answer with no variability expected. A statistical question anticipates that the data will vary, so it requires collecting multiple data points to show a distribution, such as 'How old are students in my school?' which expects ages to differ like 11, 12, or 13 across students, or 'How many pets do students have?' which anticipates varying numbers like 0, 1, 2, or 3 per student; non-statistical questions have one answer without variability, like 'How old am I?' which is just one age for one person, or 'What is 5+3?' which is always 8. For example, 'How tall are 6th graders?' is statistical because heights vary like 140 cm, 155 cm, or 170 cm among different students, creating an expected data distribution, while 'How tall is the tallest 6th grader?' is not statistical as it asks for one specific value like 170 cm without variability, and 'What is the average sleep hours?' is not statistical since the average is a single calculated number even if based on varied data. Questions 2 and 3 are statistical because 2 expects varying distances by different students, and 3 expects variation across multiple throws of the same airplane, while 1 is a single throw and 4 is math with one answer, so the correct answer is C: 2 and 3 only. A common error is thinking repeated trials like 3 are non-statistical if it's the same object, but variability is expected across trials, or classifying single events like 1 as statistical. To recognize statistical questions, read the question carefully to see what is being asked, consider if it involves multiple subjects or trials, anticipate if answers would vary across them, and classify based on whether variability is expected. Remember, the key is variability in the data, not just mentioning multiple items; even repeated actions on one item can be statistical if variation is anticipated in the results.

Question 18

A student claims that any question asking "how many" must be statistical because it involves counting. To test this reasoning, which pair of "how many" questions would best demonstrate whether this claim is correct?

  1. "How many students are in our class today?" and "How many pets do students in our class have?" (correct answer)
  2. "How many books did you read?" and "How many books did the class read total?"
  3. "How many days are in February?" and "How many days are in this month?"
  4. "How many pencils do you own?" and "How many erasers do you own?"
Explanation: This pair clearly shows that "how many" questions can be either statistical or non-statistical. "How many students are in our class today?" has one definite answer (non-statistical), while "How many pets do students in our class have?" anticipates different answers from different students (statistical). Choice B contains one statistical and one non-statistical question but less clearly demonstrates the concept. Choice C contains two non-statistical questions. Choice D contains two statistical questions.

Question 19

Which question anticipates variability in the data and would require collecting multiple data points?

  1. "What is the capital of Texas?"
  2. "What time does the first bell ring at our school today?"
  3. "How many hours of sleep do 6th graders get on a school night?" (correct answer)
  4. "What is 9×69 \times 6?"
Explanation: This question tests recognizing statistical questions as those anticipating variability in data, meaning they expect different answers from different subjects, versus non-statistical questions that have a single answer with no variability expected. A statistical question anticipates that the data will vary, so it requires collecting multiple data points to show a distribution, such as 'How old are students in my school?' which expects ages to differ like 11, 12, or 13 across students, or 'How many pets do students have?' which anticipates varying numbers like 0, 1, 2, or 3 per student; non-statistical questions have one answer without variability, like 'How old am I?' which is just one age for one person, or 'What is 5+3?' which is always 8. For example, 'How tall are 6th graders?' is statistical because heights vary like 140 cm, 155 cm, or 170 cm among different students, creating an expected data distribution, while 'How tall is the tallest 6th grader?' is not statistical as it asks for one specific value like 170 cm without variability, and 'What is the average sleep hours?' is not statistical since the average is a single calculated number even if based on varied data. The question that anticipates variability and requires multiple data points is B, as sleep hours vary among 6th graders, while A, C, and D have single answers like a fixed bell time, a capital fact, or a math result, so the correct answer is B. A common error is classifying factual or timed questions as statistical if they seem variable, like thinking the bell time varies on different days, but the question specifies 'today' for one answer without variability. To recognize statistical questions, read the question carefully to see what is being asked, consider if it involves multiple subjects or trials, anticipate if answers would vary across them, and classify based on whether variability is expected. Remember, the key is variability in the data, not just mentioning multiple items; even questions about groups can be non-statistical if seeking one specific fact.

Question 20

Is the question "How tall are the students in the 6th grade?" a statistical question?

  1. No, because height is measured in inches or centimeters
  2. No, because there is only one correct height for 6th graders
  3. Yes, because any question that starts with "How" is statistical
  4. Yes, because different 6th graders will have different heights (correct answer)
Explanation: This question tests recognizing statistical questions as those anticipating variability in data, meaning they expect different answers from different subjects, versus non-statistical questions that have a single answer with no variability expected. A statistical question anticipates that the data will vary, so it requires collecting multiple data points to show a distribution, such as 'How old are students in my school?' which expects ages to differ like 11, 12, or 13 across students, or 'How many pets do students have?' which anticipates varying numbers like 0, 1, 2, or 3 per student; non-statistical questions have one answer without variability, like 'How old am I?' which is just one age for one person, or 'What is 5+3?' which is always 8. For example, 'How tall are 6th graders?' is statistical because heights vary like 140 cm, 155 cm, or 170 cm among different students, creating an expected data distribution, while 'How tall is the tallest 6th grader?' is not statistical as it asks for one specific value like 170 cm without variability, and 'What is the average sleep hours?' is not statistical since the average is a single calculated number even if based on varied data. The question 'How tall are the students in the 6th grade?' is statistical because it anticipates different heights among students, requiring data collection from multiple students to show the variation, so the correct answer is B. A common error is thinking there is only one correct height for all 6th graders, making it non-statistical, or believing any 'How' question is automatically statistical, but the key is expected variability, not the wording alone. To recognize statistical questions, read the question carefully to see what is being asked, consider if it involves multiple subjects or trials, anticipate if answers would vary across them, and classify based on whether variability is expected. Remember, the key is variability in the data, not just mentioning multiple items; for instance, questions about groups can be non-statistical if seeking a single value like an average or maximum.