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 5. The balancing point is 5. The balancing point is 4.

Answer 1

To create a dot plot based on the data you provided, we first have to understand the frequency of hours worked by the number of students. Here's the data presented in an organized way:

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

This means we can visualize this data with a dot plot where each dot represents a student.

The dot plot would look something like this (representing each student with a dot):

```
3: •••••••
4: ••••
5: •
6: ••••
7: •••••••
```

Now we need to find the mean, which is the balancing point of the dataset. To calculate the mean, we'll sum all the hours worked by all students and then divide by the total number of students.

1. **Calculate the total hours worked:**
- For 3 hours: \(3 \times 7 = 21\)
- For 4 hours: \(4 \times 4 = 16\)
- For 5 hours: \(5 \times 1 = 5\)
- For 6 hours: \(6 \times 4 = 24\)
- For 7 hours: \(7 \times 7 = 49\)

Total hours worked = \(21 + 16 + 5 + 24 + 49 = 115\)

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

3. **Calculate the mean:**
\[
\text{Mean} = \frac{\text{Total hours}}{\text{Total students}} = \frac{115}{23} \approx 5
\]

So, the balancing point (mean) of this dataset is approximately **5**.

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