To determine which scatterplot shows a non-linear association, we'll analyze the relationships between the x and y values from each dataset. Below is the analysis of each dataset:
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First dataset:
- X values: 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
- Y values: 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
The points show a scatter with some high and low values, suggesting a possible non-linear relationship, but visual inspection would be needed to confirm.
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Second dataset:
- X values: 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
- Y values: 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
The points appear to move in a somewhat linear pattern, suggesting a positive linear association.
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Third dataset:
- X values: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- Y values: 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
Here, the points are scattered with no clear linear pattern, suggesting a more complex relationship.
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Fourth dataset:
- X values: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- Y values: 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
This set also shows a more scattered arrangement, having both high and low values across the x-range, which could indicate a non-linear relationship.
Conclusion: The first and third datasets may show non-linear associations, while the second dataset likely shows a linear association. The fourth dataset also looks non-linear. However, without a visual representation of the scatterplots, the third dataset seems to distinctly lack a clear pattern, indicating the most obvious non-linear association.
Thus, the third dataset likely demonstrates a non-linear association.