To create a dot plot for the data provided, we list the hours along a number line and place a dot for each student corresponding to the number of hours they work.
Data:
- 3 hours: 7 students (7 dots at 3)
- 4 hours: 4 students (4 dots at 4)
- 5 hours: 1 student (1 dot at 5)
- 6 hours: 4 students (4 dots at 6)
- 7 hours: 7 students (7 dots at 7)
The dot plot would look like this:
3: ●●●●●●●
4: ●●●●
5: ●
6: ●●●●
7: ●●●●●●●●
Next, to find the mean (the balancing point), we need to calculate the total number of students and the total number of hours worked.
-
Total Number of Students:
- \(7 + 4 + 1 + 4 + 7 = 23\) students.
-
Total Number of Hours Worked:
- \( (3 \times 7) + (4 \times 4) + (5 \times 1) + (6 \times 4) + (7 \times 7) \)
- \( = 21 + 16 + 5 + 24 + 49 = 115\) total hours.
-
Mean (Balancing Point):
- Mean \( = \frac{\text{Total Hours}}{\text{Total Students}} = \frac{115}{23} = 5\).
Thus, the balancing point of the dataset is 5.
Final Answer: The balancing point is 5.