To find the balancing point (mean) of the dataset, we first need to calculate the total number of students and the total "value" contributed by the number of states visited.
The data provided is:
- 1 student visited 1 state
- 3 students visited 2 states
- 1 student visited 3 states
- 3 students visited 4 states
- 6 students visited 5 states
Now, let's calculate the total number of students:
\[ \text{Total students} = 1 + 3 + 1 + 3 + 6 = 14 \]
Next, we need to calculate the total value contributed by each group of students based on the number of states they visited. We multiply the number of students by the corresponding number of states visited:
\[ \text{Total value} = (1 \times 1) + (3 \times 2) + (1 \times 3) + (3 \times 4) + (6 \times 5) \]
Calculating each term:
- \(1 \times 1 = 1\)
- \(3 \times 2 = 6\)
- \(1 \times 3 = 3\)
- \(3 \times 4 = 12\)
- \(6 \times 5 = 30\)
Now sum these values:
\[ \text{Total value} = 1 + 6 + 3 + 12 + 30 = 52 \]
Now we can find the mean (balancing point) by dividing the total value by the total number of students:
\[ \text{Mean} = \frac{\text{Total value}}{\text{Total students}} = \frac{52}{14} \approx 3.71 \]
Thus, the balancing point of the dataset is approximately 3.71.
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