To find the balancing point (mean) of the given dataset, we first need to understand the data represented in the graph. From the information provided:
- Number of states visited (X-axis): 1, 2, 3, 4, 5
- Number of students (Y-axis): 6, 3, 1, 3, 6
This means:
- 6 students 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 mean:
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Determine total number of students: \( 6 + 3 + 1 + 3 + 6 = 19 \)
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Calculate the total number of state visits (this is done by multiplying the number of students by the states they visited):
- \( 6 \times 1 = 6 \) (for 1 state)
- \( 3 \times 2 = 6 \) (for 2 states)
- \( 1 \times 3 = 3 \) (for 3 states)
- \( 3 \times 4 = 12 \) (for 4 states)
- \( 6 \times 5 = 30 \) (for 5 states)
Now, we sum these total visits: \( 6 + 6 + 3 + 12 + 30 = 57 \)
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Now we calculate the mean: \[ \text{Mean} = \frac{\text{Total state visits}}{\text{Total number of students}} = \frac{57}{19} \approx 3 \]
The balancing point of the dataset is approximately 3.