Question

The line plot below shows the number of school absences a group of students had the previous school year.

The line plot titled School Absences shows number of absences from 0 to 9. There are three X marks above 0, eight X marks above 1, four X marks above 2, two X marks above 3, and one X mark above 6.

Which statements are true? Choose all that are correct.

A.
The line plot shows that 6 students had 1 school absence.


B.
The line plot shows that most students had more than 1 school absence.


C.
The mean is greater than the median for this data set.


D.
The line plot represents 18 students.


E.
The range of these data is 9.

Answer 1

Let's analyze the line plot data to determine the accuracy of each statement based on the number of absences represented by the X marks:

1. **Count of Absences**:
- 0 absences: 3 students
- 1 absence: 8 students
- 2 absences: 4 students
- 3 absences: 2 students
- 6 absences: 1 student

Now let's evaluate each statement:

**A. The line plot shows that 6 students had 1 school absence.**
- This statement is **false**. The line plot indicates that 8 students had 1 school absence, not 6.

**B. The line plot shows that most students had more than 1 school absence.**
- This statement is **false**. The majority of students (8 out of 18) had 1 absence, which is not more than 1.

**C. The mean is greater than the median for this data set.**
- Let's calculate the mean and median:
- Total absences = (0 * 3) + (1 * 8) + (2 * 4) + (3 * 2) + (6 * 1) = 0 + 8 + 8 + 6 + 6 = 28
- Total students = 3 + 8 + 4 + 2 + 1 = 18
- Mean = Total absences / Total students = 28 / 18 ≈ 1.56 (approximately)

To find the median, we list all the absences:
- 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 6
- The median is the average of the 9th and 10th values: (1 + 1) / 2 = 1.

Thus, the mean (approximately 1.56) is indeed greater than the median (1). Therefore, this statement is **true**.

**D. The line plot represents 18 students.**
- This statement is **true**. We counted 18 students.

**E. The range of these data is 9.**
- The range is calculated as the difference between the maximum and minimum values.
- Maximum = 6, Minimum = 0, thus Range = 6 - 0 = 6, not 9. This statement is **false**.

In summary, the true statements are:
**C. The mean is greater than the median for this data set.**
**D. The line plot represents 18 students.**