6th Grade Math Quiz: Report Number Of Observations
20 questions · exam conditions
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Report Number Of ObservationsQuestion 1 of 20

A student council surveyed the school about cafeteria food preferences. They collected responses about favorite lunch items from different grade levels: 6th grade (45 responses), 7th grade (38 responses), and 8th grade (41 responses). However, when they reviewed the data, they found that 9 responses from 7th grade were duplicates where students had submitted the survey twice, and these duplicate entries needed to be removed to avoid counting the same student multiple times.

When presenting their findings to the school administration, how many total valid survey observations should the student council report?

115 unique student responses after removing duplicate submissions
124 total responses collected from all three grade levels
119 responses excluding the grade level with data problems
106 responses from only the two grades without any issues
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6th Grade Math Quiz

6th Grade Math Quiz: Report Number Of Observations

Practice Report Number Of Observations in 6th Grade 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 Report Number Of Observations, giving you a quick way to practice the rules, question types, and explanations that matter most for 6th Grade 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

A student council surveyed the school about cafeteria food preferences. They collected responses about favorite lunch items from different grade levels: 6th grade (45 responses), 7th grade (38 responses), and 8th grade (41 responses). However, when they reviewed the data, they found that 9 responses from 7th grade were duplicates where students had submitted the survey twice, and these duplicate entries needed to be removed to avoid counting the same student multiple times.

When presenting their findings to the school administration, how many total valid survey observations should the student council report?

  1. 115 unique student responses after removing duplicate submissions (correct answer)
  2. 124 total responses collected from all three grade levels
  3. 119 responses excluding the grade level with data problems
  4. 106 responses from only the two grades without any issues
Explanation: When you encounter a data collection problem involving duplicate or invalid responses, you need to carefully identify what constitutes valid, usable data for analysis. Let's work through this step-by-step. The student council initially collected responses from three grades: 6th grade (45), 7th grade (38), and 8th grade (41). This gives a total of 45+38+41=12445 + 38 + 41 = 124 responses. However, they discovered that 9 of the 7th grade responses were duplicates from students who submitted twice. To find the valid responses, you subtract the duplicate entries: 124−9=115124 - 9 = 115 unique student responses. This means 7th grade actually contributed 38−9=2938 - 9 = 29 valid responses, while 6th and 8th grades remain at 45 and 41 respectively. Choice A is correct because it accurately reflects the total valid data after removing duplicates. Choice B represents the raw total before cleaning the data, which would overcount some students. Choice C suggests excluding all 38 responses from 7th grade, but this throws away valid data from students who only responded once. Choice D only counts 6th and 8th grade responses, again discarding the valid 7th grade responses unnecessarily. Remember that in data analysis, cleaning data means removing invalid entries while preserving all valid information. Don't discard entire categories of data when you can identify and remove only the problematic entries. Always ask yourself: "What data should actually count toward my final analysis?"

Question 2

A student writes down the number of pages read each day for one week: 12, 15, 15, 10, 18, 20, 12. What is the number of observations in this data set?

  1. n=5n=5 (because there are 5 different numbers)
  2. n=8n=8
  3. n=7n=7 (correct answer)
  4. n=10n=10 (because the smallest is 10)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, distinguishing it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student being one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement one data point; or a data set like 12,14,15,16,18 has n=5 observations, counting all values in the list; each subject, measurement, or trial is one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to indicate sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students being one data point; or a data set like 5,6,6,7,7,7,8 has n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, from the 18 measurements collected. In this case, the data set has seven values listed (12, 15, 15, 10, 18, 20, 12), so the correct observation count is n=7, including duplicates. A common error here is counting unique values like n=5 for five different numbers when there are 7 total observations, or mistaking the smallest value for n=10, or arithmetic errors like counting as n=8, or omitting duplicates to count fewer. To count observations correctly, first identify the observational unit, which here is one day's pages read as one value, so one observation per value; second, count the total, which is 7 values, so n=7; third, include all, don't skip duplicates like the two 15's or two 12's, as each is a separate observation. Remember, observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions but if students are the units, n=25; or not the range, like data from 5-10 has a range of 5 but n depends on the count; the importance of n is that it's the sample size, telling how much data you have, such as n=100 being a large sample and n=5 small, and it's often the first statistic reported before mean, median, or range, as you need to know how many data points there are; common mistakes include counting the wrong things like unique options, questions, or range, omitting duplicates, or confusing the unit in the context.

Question 3

A student writes down the number of push-ups completed by each of 14 classmates. The results are:

8,10,10,12,12,12,15,15,15,15,18,18,20,208, 10, 10, 12, 12, 12, 15, 15, 15, 15, 18, 18, 20, 20

What is the number of observations?

  1. n=12n=12 (do not count repeats)
  2. n=6n=6 (unique values: 8, 10, 12, 15, 18, 20)
  3. n=20n=20 (the greatest value)
  4. n=14n=14 (correct answer)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, the student records push-ups for 14 classmates, with the list showing 14 values, so the correct observation count is n=14, counting all including repeats like the four 15's. A common error here is something like counting unique values as n=6, or omitting duplicates to count only 12, or confusing with the greatest value 20, but actually it's the total of all 14 data points. To count observations, first identify the observational unit, which here is one classmate's push-ups as one observation; second, count the total, which is 14 values in the list, so n=14; and third, include all, don't skip duplicates like counting multiple 12's as one, since each is a separate observation. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.

Question 4

A teacher surveys 28 students in a class and asks each student, "What is your favorite school lunch?" Each student gives one answer. What is the number of observations in this data set?

  1. n=n= the number of different lunches students named
  2. n=28n=28 (correct answer)
  3. n=1n=1
  4. n=2n=2 (because the question has 2 parts: favorite and lunch)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, since the teacher surveys 28 students and each gives one answer about their favorite school lunch, the correct observation count is n=28, with each student as one data point. A common error here is something like counting unique values, such as thinking n equals the number of different lunches named instead of the total students, or confusing it with the number of parts in the question, but actually it's the total data points from the 28 surveys. To count observations, first identify the observational unit, which here is one student surveyed as one observation; second, count the total, which is 28 students, so n=28; and third, include all, without skipping any since there are no duplicates mentioned in the counting. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.

Question 5

A class records the number of minutes it takes each of 16 students to run one lap. What counts as one observation in this study?​

  1. One student's lap time (one time measurement for one student) (correct answer)
  2. One minute of running
  3. All 16 students' times together
  4. The fastest time only
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, since the class records the lap time for each of 16 students, what counts as one observation is one student's lap time, which is one time measurement for one student. A common error here is something like thinking the whole set of 16 is one observation, or just the fastest time, or confusing with a unit like one minute of running, but actually each student's time is a separate data point. To count observations, first identify the observational unit, which here is one student's lap time as one observation; second, count the total, which would be 16 if all are included, but the question asks for what is one, not the total n; and third, include all individually, without combining them. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.

Question 6

A science class records the number of leaves on each of 24 bean plants. Each plant is counted once. What is the number of observations, nn, in the data set?

  1. n=1n=1 because all the plants are the same type
  2. n=12n=12 because 24 plants can be grouped into 12 pairs
  3. n=24n=24 (correct answer)
  4. n=48n=48 because plants have two sides
Explanation: This question tests reporting number of observations n (count of data points collected: students surveyed, measurements taken, values in data set), distinguishing from unique value count or range. Number of observations: count of data points collected (25 students surveyed gives n=25 observations, each student is one data point regardless of what asked; 18 heights measured gives n=18 observations, each measurement one data point; data set 12,14,15,16,18 has n=5 observations, count all values in list). The science class counted leaves on 24 bean plants, with each plant counted once—so we have 24 data points collected, making n=24 observations (each plant is one observation). The correct answer is A: n=24. Common errors include counting plant type (B: n=1 because all are bean plants), doubling for arbitrary reasons (C: n=48 for 'two sides'), or grouping plants (D: n=12 as pairs). Counting observations: (1) identify observational unit (what is one observation? one student, one measurement, one trial), (2) count total (how many plants counted? 24, so n=24), (3) include all (don't skip duplicates). The number of observations n=24 tells us we have leaf count data from 24 individual plants, providing our sample size for analyzing leaf distribution in bean plants.

Question 7

A cafeteria worker records the number of apples taken each day for 20 school days. Each day produces one number. What is the number of observations?

  1. n=20n=20 (correct answer)
  2. n=5n=5 (because there are 5 school days in a week)
  3. n=n= the range of the apple counts
  4. n=n= the number of weeks in the study
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, since the worker records the number of apples taken each day for 20 school days, with each day producing one number, the correct observation count is n=20, with each day as one data point. A common error here is something like confusing with the 5 school days in a week instead of the total 20, or thinking it's the number of weeks or the range of counts, but actually it's the total recordings over 20 days. To count observations, first identify the observational unit, which here is one day's apple count as one observation; second, count the total, which is 20 days, so n=20; and third, include all, without grouping by weeks since each day is separate. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.

Question 8

Two clubs collect data:

  • Club A surveys 22 students about their favorite sport.
  • Club B measures the arm span of 19 students.

Which club collected more observations?​

  1. They collected the same number of observations
  2. Club B
  3. Club A (correct answer)
  4. Not enough information (we need the actual survey answers)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, Club A surveys 22 students, so n=22 for them, while Club B measures 19 students, so n=19, meaning Club A collected more observations. A common error here is thinking they are the same or that you need the actual answers to compare, but actually it's just comparing the counts of data points collected, 22 versus 19. To count observations, first identify the observational unit, which for Club A is one student surveyed as one observation and for B one measurement as one; second, count the total, 22 for A and 19 for B; and third, include all, since no duplicates are mentioned. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.

Question 9

A weather station records the high temperature each day for 31 days in a month. It also records the low temperature each day, but the data set you are using includes only the high temperatures (one high per day). What is the number of observations in the data set of highs?​

  1. n=n= the number of different high temperatures
  2. n=31n=31 (correct answer)
  3. n=30n=30 (because months have about 30 days)
  4. n=62n=62 (high and low)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, the station records high temperatures for 31 days, and the data set includes only the highs with one per day, so the correct observation count is n=31, each day as one data point. A common error here is something like counting unique values such as different highs, or including lows for 62, or approximating to 30 days, but actually it's the total of 31 highs in the specified data set. To count observations, first identify the observational unit, which here is one day's high temperature as one observation; second, count the total, which is 31 days, so n=31; and third, include all, but only the highs as per the data set, not the lows. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.

Question 10

A science class records the number of sprouts on each of 30 bean plants after one week. Each plant is counted once. What is the number of observations?​

  1. n=30n=30 (correct answer)
  2. n=7n=7 (because it was after one week)
  3. n=1n=1 (one experiment)
  4. n=n= the number of different sprout counts that occurred
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, since the class records the number of sprouts on each of 30 bean plants, each counted once, the correct observation count is n=30, with each plant as one data point. A common error here is something like counting unique values, such as thinking n equals the number of different sprout counts instead of the total plants, or confusing it with the time period like one week or the experiment as a whole, but actually it's the total of 30 recordings. To count observations, first identify the observational unit, which here is one plant's sprout count as one observation; second, count the total, which is 30 plants, so n=30; and third, include all, without skipping any since each is distinct. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.

Question 11

A list shows the number of minutes 9 students spent on homework last night: 30, 25, 25, 40, 35, 30, 20, 25, 45. What is the number of observations, nn?

  1. n=9n=9 because there are 9 data points listed (correct answer)
  2. n=45n=45 because 45 is the greatest value
  3. n=6n=6 because there are 6 different values
  4. n=25n=25 because 25 appears most often
Explanation: This question tests reporting number of observations n (count of data points collected: students surveyed, measurements taken, values in data set), distinguishing from unique value count or range. Number of observations: count of data points collected (25 students surveyed gives n=25 observations, each student is one data point regardless of what asked; 18 heights measured gives n=18 observations, each measurement one data point; data set 12,14,15,16,18 has n=5 observations, count all values in list). The list shows homework minutes for 9 students: 30, 25, 25, 40, 35, 30, 20, 25, 45—counting all values gives us 9 data points, so n=9 observations (count all values including the three 25s and two 30s). The correct answer is B: there are 9 data points listed. Common errors include counting unique values only (A: n=6 different values), using the maximum value (C: n=45), or using the mode (D: n=25 appears most). Counting observations: (1) identify observational unit (what is one observation? one student, one measurement, one trial), (2) count total (how many values listed? 9, so n=9), (3) include all (don't skip duplicates: three 25s count as three observations). The number of observations n=9 tells us we have homework data from 9 students, with each student contributing one data point regardless of whether their time matches another student's.

Question 12

A data set shows the test scores of a small group of students: 70, 80, 80, 90, 90, 90, 100. What is the number of observations, nn?

  1. n=7n=7 because there are 7 scores listed (correct answer)
  2. n=100n=100 because 100 is the highest score
  3. n=30n=30 because the range is 100−70=30100-70=30
  4. n=4n=4 because there are 4 different scores
Explanation: This question tests reporting number of observations n (count of data points collected: students surveyed, measurements taken, values in data set), distinguishing from unique value count or range. Number of observations: count of data points collected (25 students surveyed gives n=25 observations, each student is one data point regardless of what asked; 18 heights measured gives n=18 observations, each measurement one data point; data set 12,14,15,16,18 has n=5 observations, count all values in list). The data set shows test scores: 70, 80, 80, 90, 90, 90, 100—counting all values gives us 7 data points, so n=7 observations (count all values including two 80s and three 90s). The correct answer is C: there are 7 scores listed. Common errors include counting unique scores only (A: n=4 different scores), calculating range (B: n=30 from 100-70), or using the maximum score (D: n=100). Counting observations: (1) identify observational unit (what is one observation? one student, one measurement, one trial), (2) count total (how many scores listed? 7, so n=7), (3) include all (don't skip duplicates: three 90s count as three observations). The number of observations n=7 tells us we have test scores from 7 students, with each student's score being one data point regardless of whether multiple students earned the same score.

Question 13

In a simple experiment, a student rolls a number cube 24 times and records the number shown each time. The student also writes down the total of all 24 results. What is the number of observations in the data set of rolls?

  1. n=24n=24 (correct answer)
  2. n=6n=6 (because a number cube has 6 sides)
  3. nn equals the total of the 24 results
  4. n=25n=25 (24 rolls plus the total)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, distinguishing it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, with each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to indicate sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, there are n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for a total of 7 data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, the student rolled the cube 24 times, recording each result, so the data set of rolls has n=24 observations, with the total being separate. A common error here is thinking n=6 for the cube's sides, but that's possible values, not rolls; or saying n is the total of the results, but that's a sum, not count; or n=25 including the total, but the data set is the rolls only. To count observations correctly, first identify the observational unit, which here is one roll's result; second, count the total, which is 24 rolls, so n=24; and third, include all rolls, but exclude summaries like the total. Remember, observations differ from possible values or sums; the importance of n is sample size, and mistakes include adding extras or confusing with attributes of the tool.

Question 14

A class records the number of minutes it takes each of 16 students to run one lap. What counts as one observation in this study?

  1. The fastest time only
  2. One minute of running
  3. All 16 students' times together
  4. One student's lap time (one time measurement for one student) (correct answer)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, since the class records the lap time for each of 16 students, what counts as one observation is one student's lap time, which is one time measurement for one student. A common error here is something like thinking the whole set of 16 is one observation, or just the fastest time, or confusing with a unit like one minute of running, but actually each student's time is a separate data point. To count observations, first identify the observational unit, which here is one student's lap time as one observation; second, count the total, which would be 16 if all are included, but the question asks for what is one, not the total n; and third, include all individually, without combining them. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.

Question 15

A coach measures the heights of 18 basketball players. Each player's height is recorded once. What is the number of observations?

  1. n=18n=18 (correct answer)
  2. n=1n=1 (because they are all on one team)
  3. n=n= the tallest height minus the shortest height
  4. n=6n=6 (one for each foot from 4 to 9)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, since the coach measures the heights of 18 basketball players, each recorded once, the correct observation count is n=18, with each height as one data point. A common error here is something like counting unique values, such as thinking n=6 for heights from 4 to 9 feet instead of the total measurements, or confusing it with the range or the fact they are on one team, but actually it's the total of 18 measurements. To count observations, first identify the observational unit, which here is one height measurement as one observation; second, count the total, which is 18 players, so n=18; and third, include all, without skipping any since each is unique in collection. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.

Question 16

A data set shows the number of pets owned by some students: 0, 1, 1, 2, 2, 2, 3, 4. How many observations are in this data set?

  1. n=5n=5 (the unique values 0–4)
  2. n=8n=8 (correct answer)
  3. n=4n=4 (because the largest number is 4)
  4. n=3n=3 (because 2 appears 3 times)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, distinguishing it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, with each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to indicate sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, there are n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for a total of 7 data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, the data set has 8 values: 0,1,1,2,2,2,3,4, so the correct observation count is n=8. A common error here is counting unique values as n=5 (0-4), but n includes repeats; or saying n=4 because the largest is 4, but that's a value, not the count; or n=3 because 2 appears three times, but that's one value's frequency; or omitting duplicates, like counting only uniques. To count observations correctly, first identify the observational unit, which here is one student's pet count; second, count the total, which is 8 values, so n=8; and third, include all, don't skip duplicates like the multiple 2's as separate observations. Remember, observations differ from unique values or maximums; the importance of n is sample size, and mistakes often involve counting uniques or frequencies instead.

Question 17

A science class conducted an experiment measuring plant growth under different light conditions. They set up 4 groups with different numbers of plants: Group 1 (fluorescent light) had 8 plants, Group 2 (LED light) had 12 plants, Group 3 (natural sunlight) had 6 plants, and Group 4 (no light) had 9 plants. During the experiment, all plants in Group 4 died before any measurements could be taken.

The students need to report their findings to the school science fair. Based on the experimental setup, how many plant observations should they report as part of their valid dataset?

  1. 35 total plants from all four experimental groups
  2. 26 plants from groups that produced measurable data (correct answer)
  3. 29 plants excluding the group with the fewest subjects
  4. 20 plants from only the two most successful groups
Explanation: Valid observations must come from plants that survived long enough to be measured. Group 1: 8 plants, Group 2: 12 plants, Group 3: 6 plants can all be reported. Group 4: 9 plants died before measurements, so these cannot be counted as valid observations. Total valid observations: 8 + 12 + 6 = 26. Choice A incorrectly includes the plants that died. Choice C excludes Group 3 incorrectly. Choice D arbitrarily excludes valid data from Groups 1 and 3.

Question 18

A librarian conducted a reading survey by asking students to report how many books they read last month. She collected responses from 5th graders and 6th graders separately. From the 5th grade, she received 34 completed surveys. From the 6th grade, she received 28 completed surveys, but later discovered that 6 of those surveys had unrealistic responses (like '500 books') that needed to be removed from the data.

When the librarian prepares her final report on student reading habits, how many total survey observations should she include in her analysis?

  1. 62 observations from both grade levels combined
  2. 68 observations including all originally submitted surveys
  3. 56 observations from only the reliable 6th grade responses
  4. 56 observations from valid responses in both grades (correct answer)
Explanation: Valid observations include only reliable data that can be used in analysis. 5th grade: all 34 surveys were usable. 6th grade: 28 original surveys - 6 unrealistic responses = 22 usable surveys. Total valid observations: 34 + 22 = 56. Choice A incorrectly includes the invalid 6th grade responses. Choice B includes all original surveys regardless of validity. Choice C only counts 6th grade data and miscounts it.

Question 19

Based on the frequency table shown, a researcher wants to report the total number of observations collected in her study about pet ownership among families. The table shows the distribution of pets per family, but the researcher realizes she needs to exclude families that refused to participate. How many observations should she report?

  1. 89 total families that were contacted for the study
  2. 76 families that provided complete pet ownership data (correct answer)
  3. 83 families excluding only those who were not home
  4. 72 families from the most common pet ownership categories
Explanation: Observations should only include families that actually participated and provided data. From the table, families with pets data: 0 pets (18), 1 pet (23), 2 pets (19), 3 pets (11), 4+ pets (5) = 76 families. The 'Refused to participate' and 'Not home' categories cannot be counted as observations since no data was collected from them. Total valid observations: 18 + 23 + 19 + 11 + 5 = 76. Choice A includes non-participants. Choice C includes some non-participants. Choice D arbitrarily excludes valid data.

Question 20

A student asks 25 classmates 3 survey questions about their after-school activities. The student plans to use each classmate as one observation (one row per student). What is nn, the number of observations?

  1. n=3n=3
  2. n=75n=75
  3. n=25n=25 (correct answer)
  4. n=28n=28 (25 classmates plus the student and teacher)
Explanation: This question tests reporting the number of observations n, which is the count of data points collected, such as students surveyed, measurements taken, or values in a data set, and distinguishes it from the unique value count or range. The number of observations is the count of data points collected; for example, if 25 students are surveyed, that gives n=25 observations, with each student as one data point regardless of what is asked; if 18 heights are measured, that gives n=18 observations, each measurement as one data point; or if a data set has values like 12,14,15,16,18, that has n=5 observations, counting all values in the list; each subject, measurement, or trial counts as one observation, not the number of questions asked or unique values, but the total data points, and its purpose is to show sample size, where a larger n means more data and a smaller n means less. For example, if you survey 25 students about their favorite subject, the number of observations is n=25, with each of the 25 students as one data point; or in a data set like 5,6,6,7,7,7,8, n=7 observations, counting all values including repeats, so three 7's count as three observations, not one, for 7 total data points; or if you measure 18 player heights, n=18, as there are 18 measurements collected. In this case, since the student asks 25 classmates 3 questions but plans to use each classmate as one observation with one row per student, the correct observation count is n=25, treating each student as one data point. A common error here is something like confusing context by multiplying students times questions to get n=75, or thinking n=3 for the questions, or adding extras like the student and teacher for 28, but actually it's the 25 classmates as units. To count observations, first identify the observational unit, which here is one classmate as one observation; second, count the total, which is 25 classmates, so n=25; and third, include all, without multiplying by questions since the unit is the student. It's important to distinguish that observations are not the same as unique values, like in a data set 5,6,6,7,7,7,8 which has 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions gives n=25 observations if students are the units, not the questions; or not the same as range, like a data range of 5-10 might suggest n=6 if listing 5,6,7,8,9,10 but n depends on the actual count, which could differ if repeated; the importance of n is that it's the sample size, telling how much data you have, like n=100 is a large sample while n=5 is small, and it's often the first statistic reported before things like mean, median, or range, since you need to know how many data points there are; common mistakes include counting the wrong things like uniques, questions, or range, omitting duplicates, or confusing the context about the unit.