To find the balancing point (or mean) for the given data, we first need to calculate the total number of students and the total weight (number of students multiplied by the number of states).
We represent the data as follows:
- One state: 6 students
- Two states: 3 students
- Three states: 1 student
- Four states: 3 students
- Five states: 6 students
Next, we calculate the total number of students and their corresponding weights:
- One state: \(1 \times 6 = 6\)
- Two states: \(2 \times 3 = 6\)
- Three states: \(3 \times 1 = 3\)
- Four states: \(4 \times 3 = 12\)
- Five states: \(5 \times 6 = 30\)
Now, we sum these products to find the total weight:
\[ \text{Total weight} = 6 + 6 + 3 + 12 + 30 = 57 \]
Next, we calculate the total number of students:
\[ \text{Total number of students} = 6 + 3 + 1 + 3 + 6 = 19 \]
Finally, to find the mean (balancing point):
\[ \text{Mean} = \frac{\text{Total weight}}{\text{Total number of students}} = \frac{57}{19} \approx 3 \]
Thus, the balancing point (mean) of the given data is approximately 3.