To create a dot plot for the given data and find the mean (balancing point), follow these steps:
Step 1: Create the Dot Plot
The data provided:
- 0 pets: 6 students
- 1 pet: 4 students
- 2 pets: 1 student
- 3 pets: 4 students
- 4 pets: 6 students
Dot Plot:
0: • • • • • •
1: • • • •
2: •
3: • • • •
4: • • • • • •
Step 2: Calculate the Mean
To find the mean, we will use the formula for the mean: \[ \text{Mean} = \frac{\text{Total of all data points}}{\text{Total number of data points}} \]
Total of all data points:
- For 0 pets: \(0 \times 6 = 0\)
- For 1 pet: \(1 \times 4 = 4\)
- For 2 pets: \(2 \times 1 = 2\)
- For 3 pets: \(3 \times 4 = 12\)
- For 4 pets: \(4 \times 6 = 24\)
Now sum these products: \[ 0 + 4 + 2 + 12 + 24 = 42 \]
Total number of data points (students): \[ 6 + 4 + 1 + 4 + 6 = 21 \]
Step 3: Calculate the Mean
Now substitute into the formula: \[ \text{Mean} = \frac{42}{21} = 2 \]
Conclusion
The balancing point of the data is 2.