Question

Use the table to answer the question.

Number of Hours Students Work Per Week
Hours Per Week Number of Students
3 7
4 4
5 1
6 4
7 7
Create a dot plot for the data in the table. Use the mean to find the balancing point of the dataset.

(1 point)
Responses

The balancing point is 4.
The balancing point is 4.

The balancing point is 5.
The balancing point is 5.

The balancing point is 7.
The balancing point is 7.

The balancing point is 1.
The balancing point is 1.

Answer 1

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.**