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 1.
The balancing point is 1.

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

The balancing point is 7.
The balancing point is 7.
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Answer 1

To create a dot plot for the data provided, we will represent each hour of work with a dot corresponding to the number of students who work that number of hours:

- For 3 hours: 7 dots
- For 4 hours: 4 dots
- For 5 hours: 1 dot
- For 6 hours: 4 dots
- For 7 hours: 7 dots

The dot plot would look like this:

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

Next, we calculate the mean (average) number of hours worked by the students. Here's how it's done:

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

2. Calculate the total number of hours worked by all students:
\( (3 \times 7) + (4 \times 4) + (5 \times 1) + (6 \times 4) + (7 \times 7) \)
\[
= 21 + 16 + 5 + 24 + 49 = 115 \text{ total hours}
\]

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

Thus, the mean number of hours students work per week (the balancing point) is 5.

### Answer
The balancing point is 5.