Recognize Statistical Questions
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6th Grade Math › Recognize Statistical Questions
Rewrite the non-statistical question as a statistical question.
Non-statistical: "How many minutes did I practice piano yesterday?"
Which rewrite is statistical?
"How many minutes are in 1 hour?"
"How many minutes do students in my class practice piano on a typical day?"
"How many minutes did I practice piano yesterday, rounded to the nearest minute?"
"How many minutes did I practice piano yesterday at 6:00 PM?"
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.
Which of the following is a statistical question?
"What is the temperature right now in our classroom?"
"What are the heights of the players on the basketball team?"
"What is the height of the tallest player on the basketball team?"
"What day of the week is it today?"
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, 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.
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?
Neither A nor B is statistical
A is not statistical and B is statistical
Both A and B are statistical
A is statistical and B is not 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), 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.
A student wrote the question: "How old am I?" Rewrite it as a statistical question.
"What is $2026-2014$?"
"How old will I be next year?"
"How old are students in my grade?"
"What is my birthday?"
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. 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.
Which question anticipates variability in the data (so it is statistical)?
"What is the temperature right now in our classroom?"
"What day of the week is it today?"
"What is the height of the tallest player on the basketball team?"
"How tall are the players on the basketball team?"
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 question 'How tall are the players on the basketball team?' anticipates variability because heights differ among players, requiring a distribution of data, while the others seek single specific values, so choice C is correct. A common error is mistaking questions like 'What is the height of the tallest player?' as statistical because it involves a group, but it asks for one value without variability; another mistake is thinking current measurements like temperature have variability when they are fixed at a moment. 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.
A student wrote these questions for a class survey. Which questions are statistical questions (they expect answers to vary)?
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"How old are students in my school?"
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"How old am I?"
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"How many hours do 6th graders sleep on a school night?"
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"What is $5+3$?"
1, 2, and 3 only
1 and 3 only
2 and 4 only
All four questions 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), require collecting multiple data points showing distribution, such as 'How old are students in my school?' which expects variability in ages like 11, 12, 13 across students, or 'How many pets do students have?' anticipating varying numbers like 0, 1, 2 per student. For example, 'How tall are 6th graders?' is statistical because heights vary (140 cm, 155 cm, etc.), while 'How tall is the tallest 6th grader?' is not, as it seeks one specific value like 170 cm with no variability. In this case, questions 1 and 3 are statistical because they expect varying ages and sleep hours among multiple students, while 2 is about one person with one age and 4 is a math fact with one answer, so the correct choice is A: 1 and 3 only. A common error is thinking question 2 is statistical because it involves age, but it lacks variability as it's about a single individual. To recognize statistical questions, read carefully to see if multiple subjects are involved, anticipate if answers would vary across them, and classify based on expected variability rather than topic alone. Remember, the key is variability in data, not just mentioning a group—if the question seeks a single answer without distribution, it's not statistical.
Which question anticipates variability in the data and would require collecting multiple data points?
"What is $9 \times 6$?"
"How many hours of sleep do 6th graders get on a school night?"
"What time does the first bell ring at our school today?"
"What is the capital of Texas?"
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.
A science class asks these questions while doing a paper-airplane experiment:
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"How far did my airplane fly on one throw?"
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"How far do students' airplanes fly when each student throws once?"
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"How far do airplanes fly when the same airplane is thrown 10 times?"
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"What is $30 \div 5$?"
Which questions are statistical?
2 and 3 only
1, 2, 3, and 4
1 and 4 only
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.
Which question anticipates variability in the data (different answers from different people)?
"What is the date today?"
"What is $9+6$?"
"How many sides does a triangle have?"
"How many minutes does it take students to finish their math homework?"
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, such as 'How old are students in my school?' with varying ages (11, 12, 13), or 'How many pets do students have?' expecting different counts (0, 1, 2). For example, 'How tall are 6th graders?' is statistical with height variation, but 'How tall is the tallest 6th grader?' is not (one value), and 'What is average sleep hours?' is not, seeking a single average. The correct choice is C, as it anticipates varying homework times from different students, unlike A (math), B (date), or D (triangle sides), which have fixed answers. An error might be choosing B, thinking dates vary, but it's a single fact without data collection or variability. To recognize, assess if answers would differ across individuals or instances, classifying based on expected distribution. Key: variability is crucial, not just the question being broad—fixed facts remain non-statistical.
A student wants to ask a statistical question that would require collecting data from several people. Which question works best?
"What is the average age of students in my class?"
"How long does it take students in my class to get to school?"
"How old am I?"
"What is $12 \div 3$?"
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 ages varying (11, 12, 13), or 'How many pets do students have?' expecting different numbers (0, 1, 2). For instance, '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 seeks one number despite underlying data variation. The best choice is D, as it requires collecting varying travel times from several students, making it statistical, unlike A (single age), B (math fact), or C (single average). A common mistake is selecting C, assuming averages involve data collection, but the question itself asks for a single value, not the variable data. To identify, check if the question necessitates gathering multiple varying responses from people, not just computing a summary. Remember, the key is the question anticipating a distribution of answers, not merely requiring data to find one answer.