To determine which scatterplot shows a linear association among the given sets of data, we can analyze the pattern of the points in each pair of (x, y) values.
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First Set of Points:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
Analysis: The values of y do not appear to change in a consistent manner with the values of x. The scatterplot would likely have a varied trend.
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Second Set of Points:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
Analysis: This set also does not show a consistent increase or decrease. The points would likely be scattered without a linear trend.
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Third Set of Points:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700
Analysis: Similar to the previous sets, the data points do not show a linear trend.
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Fourth Set of Points:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
Analysis: This set resembles a possible linear trend more than the others, especially since there appears to be some consistency in the values at certain intervals.
Based on the analysis, the fourth scatterplot (with the last set of (x, y) values) is most likely to show a linear association, but without plotting them, it’s hard to assert definitively. However, it shows the clearest pattern suggesting a trend compared to the other sets. Therefore, the fourth set is the most likely candidate for exhibiting a linear association.