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.

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 $$45 + 38 + 41 = 124$$ 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: $$124 - 9 = 115$$ unique student responses. This means 7th grade actually contributed $$38 - 9 = 29$$ 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?"

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 teacher surveyed 28 students, each providing one answer, so the correct observation count is n=28. A common error here is counting the number of different lunches named as n, but that would be the count of unique values, not the total observations; or thinking n=2 because there is one question and one answer, but n counts the total data points from all students, not per student; or assuming n=1 as if it's a single survey, but each student's response is a separate observation. To count observations correctly, first identify the observational unit, which here is one student's answer; 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 a way that changes the count. Remember, observations are not the same as unique values, like in a data set with 5,6,6,7,7,7,8 having 4 unique values but n=7 observations; or not the same as questions, like surveying 25 students with 5 questions but n=25 if students are the units; or not the same as range, like a data range of 5-10 having a difference of 5 but n depending on the actual count; the importance of n is that it shows 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 things like mean or median, since you need to know how many data points there are; common mistakes include counting the wrong things like unique items, questions, or range, omitting duplicates, or confusing the context about what the unit is.

Valid observations can only include days when data was actually collected successfully. Monday: 23, Tuesday: 31, Thursday: 19, Friday: 27. Wednesday must be excluded because no data was recorded due to equipment malfunction. Total valid observations: 23 + 31 + 19 + 27 = 100. Choice A incorrectly includes an estimate for Wednesday. Choice B incorrectly includes Wednesday and adds extra observations. Choice D incorrectly excludes Monday when that data was valid.

When you encounter word problems about data collection, focus carefully on what actually happened versus what was planned. The key is identifying which students successfully completed the full assessment.

Let's track the successful observations: Class A had 22 students who completed the push-up test on Monday. Class B had 25 students who also finished on Monday. Class C was interrupted by a fire drill, but 16 students did complete the assessment before the interruption. Adding these up: $$22 + 25 + 16 = 63$$ students who successfully completed the full push-up assessment.

Answer A is correct because it accurately counts only the students who actually finished the assessment (63 total). Answer B (68 students) incorrectly uses the original planned numbers, including all 21 students from Class C even though only 16 were tested. Answer C (47 students) makes the mistake of excluding Class C entirely, even though 16 students from that class did complete the assessment. Answer D (52 students) also incorrectly excludes all of Class C's data, counting only Classes A and B.

The trap in this problem is deciding how to handle incomplete data. Some answers tempt you to either ignore the partial class completely or count students who weren't actually tested. Always read carefully to distinguish between what was planned and what actually occurred, then count only the successful observations.

Observations are counted based on successful measurement days, regardless of weather conditions. Week 1: 6 successful measurement days (7 days - 1 equipment failure). Week 2: 5 successful measurement days (7 days - 2 power outages). Total observations: 6 + 5 = 11. Choice A incorrectly counts all calendar days. Choice C incorrectly focuses on rainy days rather than measurement days. Choice D miscounts by only excluding one failed day.

To find the total observations Ms. Rodriguez can report, we need to count the observations from Class A and Class C only (since Class B data was lost). Class A has 15 observations (P, P, C, P, S, M, C, P, C, S, P, M, P, C, P). Class C has 14 observations (M, P, C, S, P, M, C, P, S, M, C, P, M, S). Total: 15 + 14 = 29 observations. Choice A incorrectly includes all three classes. Choice B miscounts the remaining observations. Choice D only counts one class instead of both remaining classes.

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.

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.

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.