Recognize Statistical Questions - 6th Grade Math

1. 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?
   Answer: A is not statistical and B is statistical 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.
2. Which list contains only statistical questions?
   Answer: "How many minutes do students spend on homework each night?" and "What are students' favorite school subjects?" 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 list in B contains only statistical questions because both ask about varying homework times and favorite subjects among students, while the other lists include non-statistical ones like counts, math, tallest, or fixed facts, so the correct answer is B. A common error is assuming lists with group-related questions are all statistical, like claiming the tallest student question varies, but it seeks one value without distribution. 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; ensure all questions in a list anticipate variation to classify the list as only statistical.
3. Is the question "What is the weather today in our town?" a statistical question?
   Answer: No, because it is asking about one day with one set of conditions 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.
4. A student wrote the question: "How old am I?" Rewrite it as a statistical question.
   Answer: "How old are students in my grade?" 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. To rewrite 'How old am I?' as statistical, choice A changes it to 'How old are students in my grade?' which anticipates varying ages among students, while B, C, and D remain single answers, so the correct answer is A. A common error is thinking personal future questions like 'How old will I be next year?' are statistical due to time, but they have one determined 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; rewriting to include a group with expected variation makes it statistical.
5. Rewrite the non-statistical question as a statistical question. Non-statistical: "How many minutes did I practice piano yesterday?" Which rewrite is statistical?
   Answer: "How many minutes do students in my class practice piano on a typical day?" 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.
6. Compare the two questions: A) "What is the weather today in our town?" B) "What is the weather each day this week in our town?" Which statement is correct?
   Answer: A is not statistical and B is statistical 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?' expecting age variation (11, 12, 13), or 'How many pets do students have?' with differing numbers (0, 1, 2). For example, 'How tall are 6th graders?' is statistical due to varying heights, but 'How tall is the tallest 6th grader?' is not (single value), and 'What is average sleep hours?' is not, as it's one number. Here, A is not statistical (single day's weather), while B is, anticipating varying weather over multiple days, so the correct statement is B. A common mistake is thinking both are statistical because they involve weather, but A lacks variability across multiple points. To compare, consider the scope—single instance vs. multiple with expected differences. Key: questions over time or trials can be statistical if variation is anticipated, unlike one-time facts.
7. Rewrite the non-statistical question as a statistical question. Non-statistical: "How many minutes did I practice piano yesterday?" Which rewrite is statistical?​
   Answer: "How many minutes do students in my class practice piano on a typical day?" 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.
8. 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 $30 \div 5$?" Which questions are statistical?
   Answer: 2 and 3 only 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.
9. 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?
   Answer: "How many students are in our class today?" and "How many pets do students in our class have?" 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.
10. 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?
    Answer: "How many pets do students in our class have?" and "How many pets does Sarah have?" 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.
11. 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?
    Answer: A is not statistical and B is statistical 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.
12. 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?
    Answer: "What is the official start time for first period at our school?" 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.
13. A student wants to ask a statistical question about lunch. Which question is statistical?
    Answer: "How many different fruits do students choose at lunch each day?" 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 statistical question about lunch is D because it asks about different fruits chosen by students each day, expecting variability in choices, while A, B, and C have single answers like one person's lunch, a math fact, or today's fixed menu, so the correct answer is D. A common error is assuming questions about daily events are statistical due to potential change over time, like claiming the lunch menu question varies, but it asks for one specific day without expected 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; questions about specific single facts, even if related to groups, are not statistical.
14. 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?
    Answer: The student confused the lunch period duration with individual eating time variations 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.
15. 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 $12-5$?" 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)?
    Answer: 1 and 4 only 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.
16. Which of the following questions is not statistical?
    Answer: "What is the sum of $18+27$?" 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 question 'What is the sum of 18+27?' is not statistical because it has one fixed answer with no variability, while the others expect distributions like varying pages read, times, or heights, so choice D is correct. A common error is assuming all questions about students are statistical, but math calculations lack data variation; another mistake is not recognizing that phrases like 'each' or 'of each' imply collecting multiple varying data points. 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.
17. 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?
    Answer: "What is the exact distance from the school's front door to the flagpole?" 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.
18. Which of the following is a statistical question?
    Answer: "What are the heights of the players on the basketball team?" 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, such as 'How old are students in my school?' expecting varying ages like 11, 12, 13, or 'How many pets do students have?' anticipating different counts like 0, 1, 2 across students. For example, 'How tall are 6th graders?' is statistical with heights varying (140 cm, 155 cm, etc.), while 'How tall is the tallest 6th grader?' is not, seeking one value like 170 cm, and 'What is average sleep hours?' is not statistical as it asks for a single calculated number. The correct choice is C, as it asks for the heights of players, expecting a distribution of varying measurements, unlike the others which seek single answers like one height, temperature, or day. A frequent error is picking A, thinking it involves a group, but it asks for a specific single value (tallest) without variability in the answer. To recognize, examine if the question implies collecting multiple varying data points or just one fixed answer. Key point: even questions about groups aren't statistical if they target a single metric without accounting for distribution.
19. 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?
    Answer: "What was the highest score on yesterday's math test?" and "What scores did students earn on yesterday's math test?" 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.
20. Which set contains only statistical questions?
    Answer: "How many siblings do students in my grade have?" and "How many minutes do students spend on screens after school?" 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, such as 'How old are students in my school?' expecting ages like 11, 12, 13 to vary, or 'How many pets do students have?' with numbers differing (0, 1, 2). For example, 'How tall are 6th graders?' is statistical with varying heights, but 'How tall is the tallest 6th grader?' is not (one value), and 'What is average sleep hours?' is not, seeking a single average. Set B contains only statistical questions, both expecting variability in siblings and screen time across students, unlike the others with non-statistical pairs like math facts or single values. An error is selecting D, thinking specifics like tallest or score are variable, but they ask for single answers. To evaluate sets, verify each question individually for variability anticipation. Key: only sets where all questions expect data distributions qualify, not those with any single-answer questions.

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