To find the balancing point (mean) of the dataset, we first need to calculate the total number of hours worked by all students and then divide it by the total number of students.
Step 1: Calculate the total number of students
From the table:
- 7 students work 3 hours = 3 * 7 = 21 hours
- 4 students work 4 hours = 4 * 4 = 16 hours
- 1 student works 5 hours = 1 * 5 = 5 hours
- 4 students work 6 hours = 4 * 6 = 24 hours
- 7 students work 7 hours = 7 * 7 = 49 hours
Now sum all of these values:
\[ \text{Total hours} = 21 + 16 + 5 + 24 + 49 = 115 \text{ hours} \]
Step 2: Calculate the total number of students
\[ \text{Total Students} = 7 + 4 + 1 + 4 + 7 = 23 \text{ students} \]
Step 3: Calculate the mean
\[ \text{Mean} = \frac{\text{Total hours}}{\text{Total Students}} = \frac{115}{23} \approx 5 \]
Conclusion
The balancing point (mean) of the dataset is approximately 5.
Therefore, the correct response is:
The balancing point is 5.