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 7.
The balancing point is 7.

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

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

The balancing point is 5.

Answer 1

To find the balancing point, we first need to calculate the mean (or average) of the dataset. This involves taking into account the number of students working each hour.

From the table provided, the data can be summarized as follows:

- 3 hours: 7 students
- 4 hours: 4 students
- 5 hours: 1 student
- 6 hours: 4 students
- 7 hours: 7 students

**Calculating the mean:**

1. **Multiply each hour by the number of students:**
- \(3 \times 7 = 21\)
- \(4 \times 4 = 16\)
- \(5 \times 1 = 5\)
- \(6 \times 4 = 24\)
- \(7 \times 7 = 49\)

2. **Add these results together:**
- Total = \(21 + 16 + 5 + 24 + 49 = 115\)

3. **Count the total number of students:**
- Total number of students = \(7 + 4 + 1 + 4 + 7 = 23\)

4. **Calculate the mean:**
- Mean = \(\frac{Total\,value}{Total\,students} = \frac{115}{23} \approx 5\)

Thus, the mean, or balancing point of the dataset, is approximately **5**.

Therefore, the correct response is:
**The balancing point is 5.**