To determine which scatterplot shows a linear association, we need to analyze the provided data sets for patterns in the relationship between \(x\) and \(y\).
Let's summarize the data sets you provided:
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First Data Set:
- \(x\): 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- \(y\): 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
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Second Data Set:
- \(x\): 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- \(y\): 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700
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Third Data Set:
- \(x\): 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- \(y\): 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
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Fourth Data Set:
- \(x\): 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- \(y\): 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
Analyzing for Linear Association:
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First Data Set:
- Possible linear trend as \(y\) increases with \(x\), though there are points that seem out of trend.
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Second Data Set:
- More scattered values with no clear linear trend, particularly with the values dropping sharply in the mid-range.
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Third Data Set:
- Data does not show a linear trend; values fluctuate without a consistent increase or decrease.
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Fourth Data Set:
- Shows a more consistent pattern, with some points that align vertically suggesting a stronger linear association from the midpoint.
Conclusion:
- The first and fourth data sets have the potential for linear relationships, but the fourth dataset appears to have clearer linearity than the first on close observation. However, without visual scatterplots plotted, the most definitive conclusion is challenging.
Thus, based on the descriptions and observations:
- If asked to choose: The fourth data set is likely the one that shows a linear association, as it appears more consistently aligned compared to the others.