To determine which scatterplot shows a non-linear association, we can look at the relationship between the x-values and y-values in each set. Here's a brief analysis of each dataset based on the information given:
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First Set:
- x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- y: 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
- Analysis: The y-values do not consistently increase or decrease with the x-values, showing some level of fluctuation which suggests a possible non-linear relationship.
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Second Set:
- x: 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
- y: 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
- Analysis: Here, the y-values mostly increase as x-values increase, indicating a linear association.
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Third Set:
- x: 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
- y: 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
- Analysis: This set shows a clear fluctuation in the y-values which indicates a possible non-linear relationship.
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Fourth Set:
- x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- y: 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
- Analysis: The y-values seem to fluctuate significantly, which also suggests a non-linear relationship.
Conclusion: Both the first and third sets appear to show signs of non-linear associations due to the fluctuating nature of the y-values relative to the x-values. However, the third set likely has the most prominent non-linear relationship because of the drastic changes in y-values, particularly with values dropping (e.g., 100, 25, 40) compared to more consistent changes in the second set.
Thus, the third scatterplot is likely to exhibit the most pronounced non-linear association.