Question

which two points should the trend line go through to best represent the data given in this scatterplot? (30,69) and (71,78) (37,30) and (48,103) (40,60) and (71,78) (40,60) and (80,120)

Explanation:

Step1: Analyze the first option

For the points \((30,69)\) and \((71,78)\), the point \((30,69)\) is not near the middle - range of the data points in terms of \(x\) and \(y\) values.

Step2: Analyze the second option

For the points \((37,30)\) and \((48,103)\), the point \((37,30)\) has a \(y\) - value that is much lower than most of the data points, so it does not represent the central tendency of the data.

Step3: Analyze the third option

For the points \((40,60)\) and \((71,78)\), both points are in the middle - range of the \(x\) and \(y\) values of the data points. The \(x\) values \(40\) and \(71\) are within the range of \(x\) values of the data, and the \(y\) values \(60\) and \(78\) are also within the middle range of \(y\) values.

Step4: Analyze the fourth option

For the points \((40,60)\) and \((80,120)\), while \((40,60)\) is a good candidate, the point \((80,120)\) has a \(y\) - value that is on the higher side compared to the central tendency of the data.

Answer:

\((40,60)\) and \((71,78)\) (i.e., the third option \(\bigcirc(40,60)\) and \((71,78)\))