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In 2009, the city’s schools received an average rating of 7.0 among all survey responders in the category of Engagement.: No
If in 2011 the schools received a rating below 7.0 in a particular category, there is a 67% probability that this rating was given by students.: Yes
In 2011, the average rating that the city’s schools were given by students and teachers combined for Academic Expectations was greater than the rating the schools were given for Academic Expectations by parents.: No
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Data Insights (DI) Butler 2023-24 [Question #174, Date: Dec-27-2023] [Click here for Details]
The table shows the results for the years 2009 and 2011 of a citywide survey of students, parents, and teachers regarding the city’s schools. In total, 14,700 teachers, 63,200 students, and 41,600 parents responded in 2009, and 15,300 teachers, 67,600 students, and 40,700 parents responded in 2011. Survey responders graded the city’s schools on a scale of 1 to 10 in 4 major categories.
Students | Parents | Teachers | ||||
| Category | 2009 | 2011 | 2009 | 2011 | 2009 | 2011 |
|---|---|---|---|---|---|---|
| Academic Expectations | 7.2 | 7.5 | 8.1 | 7.8 | 7.6 | 8.2 |
| Communication | 5.8 | 6.1 | 7.6 | 7.9 | 6.5 | 6.4 |
| Engagement | 6.4 | 6.7 | 7.4 | 7.8 | 7.2 | 7.3 |
| Safety and Respect | 7.1 | 7.2 | 8.4 | 8.6 | 6.8 | 7 |
For each of the following statements, select Yes if the statement is true based on the information in the table. Otherwise, select No.
| Yes | No | |
| In 2009, the city’s schools received an average rating of 7.0 among all survey responders in the category of Engagement. | ||
| If in 2011 the schools received a rating below 7.0 in a particular category, there is a 67% probability that this rating was given by students. | ||
| In 2011, the average rating that the city’s schools were given by students and teachers combined for Academic Expectations was greater than the rating the schools were given for Academic Expectations by parents. |
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Official Answer
In 2009, the city’s schools received an average rating of 7.0 among all survey responders in the category of Engagement.: No
If in 2011 the schools received a rating below 7.0 in a particular category, there is a 67% probability that this rating was given by students.: Yes
In 2011, the average rating that the city’s schools were given by students and teachers combined for Academic Expectations was greater than the rating the schools were given for Academic Expectations by parents.: No
01 Jan 2024, 10:53
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Official Explanation
Statement 1: Seven is the straight average between the three average scores (6.4, 7.4, and 7.2) given by students, parents, and teachers, respectively. However, a different number of students, parents, and teachers responded, so a weighted average should be considered instead. Without performing the exact calculations, you can tell that, for instance, the 63,200 students weigh more heavily on the average than the 14,700 teachers do, so they will pull the average down compared to the straight average. (The actual average turns out to be 6.8.)
Answer: No
Statement 2: In 2011, the city’s schools received three ratings below 7.0: by students in the category of Communication and the category of Engagement, and by teachers in the category of Communication. Thus, among these three ratings, the probability that one of them was by students is 67% (two out of three).
Answer: Yes
Statement 3: The same principle applies here as in the first question. The straight average of 7.5 (the students’ grade) and 8.2 (the teachers’ grade) is 7.85. However, the weighted average is 7.61, which is lower than the parents’ grade of 7.8.
Answer: No
Statement 1: Seven is the straight average between the three average scores (6.4, 7.4, and 7.2) given by students, parents, and teachers, respectively. However, a different number of students, parents, and teachers responded, so a weighted average should be considered instead. Without performing the exact calculations, you can tell that, for instance, the 63,200 students weigh more heavily on the average than the 14,700 teachers do, so they will pull the average down compared to the straight average. (The actual average turns out to be 6.8.)
Answer: No
Statement 2: In 2011, the city’s schools received three ratings below 7.0: by students in the category of Communication and the category of Engagement, and by teachers in the category of Communication. Thus, among these three ratings, the probability that one of them was by students is 67% (two out of three).
Answer: Yes
Statement 3: The same principle applies here as in the first question. The straight average of 7.5 (the students’ grade) and 8.2 (the teachers’ grade) is 7.85. However, the weighted average is 7.61, which is lower than the parents’ grade of 7.8.
Answer: No
General Discussion
