To find the mean (or balancing point) of the data, we first need to calculate the total number of pets owned by all students and the total number of students.
Using the provided data:
- Number of Pets: 0, 1, 2, 3, 4
- Number of Students: 6, 4, 1, 4, 6
Now, we can compute the total number of pets owned by all students:
\[ \text{Total Pets} = (0 \times 6) + (1 \times 4) + (2 \times 1) + (3 \times 4) + (4 \times 6) \]
Calculating each term:
- \(0 \times 6 = 0\)
- \(1 \times 4 = 4\)
- \(2 \times 1 = 2\)
- \(3 \times 4 = 12\)
- \(4 \times 6 = 24\)
Now, summing these up gives:
\[ \text{Total Pets} = 0 + 4 + 2 + 12 + 24 = 42 \]
Next, we calculate the total number of students:
\[ \text{Total Students} = 6 + 4 + 1 + 4 + 6 = 21 \]
Finally, we find the mean by dividing the total number of pets by the total number of students:
\[ \text{Mean} = \frac{\text{Total Pets}}{\text{Total Students}} = \frac{42}{21} = 2 \]
Thus, the balancing point of the data is 2.