Question

Read the passage and answer the following question(s).

Middle School Attendance

The principal at a middle school was concerned about the number of student absences during the fall semester. She selected a group of 20 students to experiment with a "phone-buddy" system for preventing absences during the spring semester. The dot plots show the number of absences for each of the 20 students in each semester.

The dot plot for Fall Semester Attendance has one dot between 0 and 2, one dot at 2, one dot between 2 and 4, two dots at 4, one dot between 4 and 6, two dots between 6 and 8, three dots at 8, two dots between 8 and 10, one dot between 10 and 12, one dot at 12, two dots at 14, one dot at 16, and one dot between 16 and 18. The dot plot for Spring Semester Attendance has three dots at 0, two dots between 0 and 2, one dot at 2, one dot between 2 and 4, two dots at 4, two dots at 6, one dot between 6 and 8, two dots between 8 and 10, two dots between 12 and 14, two dots at 14, one dot between 14 and 16, and one dot between 18 and 20.

What is the difference between the means of the data for the two semesters?

A.
2.5

B.
1.5

C.
2

D.
3

Answer 1

To find the difference between the means of the two semesters' attendance data, we first need to calculate the mean number of absences for each semester.

**Fall Semester Attendance:**
1. We analyze the data points from the dot plot:
- 0-2: 1 student (average = 1) = 1 * 1 = 1
- 2: 1 student = 1 * 2 = 2
- 2-4: 1 student (average = 3) = 1 * 3 = 3
- 4: 2 students = 2 * 4 = 8
- 4-6: 1 student (average = 5) = 1 * 5 = 5
- 6-8: 2 students (average = 7) = 2 * 7 = 14
- 8: 3 students = 3 * 8 = 24
- 8-10: 2 students (average = 9) = 2 * 9 = 18
- 10-12: 1 student (average = 11) = 1 * 11 = 11
- 12: 1 student = 1 * 12 = 12
- 14: 2 students = 2 * 14 = 28
- 16: 1 student (average = 17) = 1 * 17 = 17
- 16-18: 1 student (average = 17) = 1 * 17 = 17

2. Summing these products:
- Total absences for Fall = 1 + 2 + 3 + 8 + 5 + 14 + 24 + 18 + 11 + 12 + 28 + 17 + 17 = 147

3. The mean for Fall:
\( \text{Mean} = \frac{\text{Total absences}}{\text{Number of students}} = \frac{147}{20} = 7.35 \)

**Spring Semester Attendance:**
1. Analyzing the dot plot data for spring:
- 0: 3 students = 3 * 0 = 0
- 0-2: 2 students (average = 1) = 2 * 1 = 2
- 2: 1 student = 1 * 2 = 2
- 2-4: 1 student (average = 3) = 1 * 3 = 3
- 4: 2 students = 2 * 4 = 8
- 6: 2 students = 2 * 6 = 12
- 6-8: 1 student (average = 7) = 1 * 7 = 7
- 8-10: 2 students (average = 9) = 2 * 9 = 18
- 12-14: 2 students (average = 13) = 2 * 13 = 26
- 14: 2 students = 2 * 14 = 28
- 14-16: 1 student (average = 15) = 1 * 15 = 15
- 18-20: 1 student (average = 19) = 1 * 19 = 19

2. Summing these products:
- Total absences for Spring = 0 + 2 + 2 + 3 + 8 + 12 + 7 + 18 + 26 + 28 + 15 + 19 = 120

3. The mean for Spring:
\( \text{Mean} = \frac{120}{20} = 6 \)

**Finding the difference between the means:**
- Mean difference = \( 7.35 - 6 = 1.35 \)

So the closest option corresponding to this difference is:

### Answer: B. 1.5