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:
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Calculate the total number of students: \( 7 + 4 + 1 + 4 + 7 = 23 \) students.
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Calculate the total number of hours worked by all students: \( (3 \times 7) + (4 \times 4) + (5 \times 1) + (6 \times 4) + (7 \times 7) \) \[ = 21 + 16 + 5 + 24 + 49 = 115 \text{ total hours} \]
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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.