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Two-variable data: Models and scatterplots SAT question

Math · Problem-Solving and Data Analysis · Medium · Answer it here, explanation included.

The figure presents a scatterplot titled “Income and Percent of Total Expenses Spent on Programs for Ten Charities in 2011.” The horizontal axis is labeled “Total income,” in millions of dollars, and the numbers zero through 7,000, in increments of 1,000, are indicated. The vertical axis is labeled “Percent of total expenses spent on programs” and the numbers 70 through 95, in increments of 5, are indicated.

The 10 data points on the graph are presented in the following list. All data are approximate.

1,300 million dollars; 74 percent.
1,500 million dollars; 82 percent.
1,550 million dollars; 84 percent.
1,550 million dollars; 85 percent.
3,300 million dollars; 84 percent.
3,400 million dollars; 92 percent.
4,200 million dollars; 91 percent.
4,500 million dollars; 89 percent.
4,500 million dollars; 80 percent.
6,000 million dollars; 87 percent.

The line of best fit is also shown and passes through the following coordinates on the graph. All values are approximate.

1,200 million dollars; 81 percent.
3,500 million dollars; 85 percent.
5,000 million dollars; 88 percent.

The scatterplot above shows data for ten charities along with the line of best fit. For the charity with the greatest percent of total expenses spent on programs, which of the following is closest to the difference of the actual percent and the percent predicted by the line of best fit?

ExplanationShow

Choice B is correct. The charity with the greatest percent of total expenses spent on programs is represented by the highest point on the scatterplot; this is the point that has a vertical coordinate slightly less than halfway between 90 and 95 and a horizontal coordinate slightly less than halfway between 3,000 and 4,000. Thus, the charity represented by this point has a total income of about $3,400 million and spends about 92% of its total expenses on programs. The percent predicted by the line of best fit is the vertical coordinate of the point on the line of best fit with horizontal coordinate $3,400 million; this vertical coordinate is very slightly more than 85. Thus, the line of best fit predicts that the charity with the greatest percent of total expenses spent on programs will spend slightly more than 85% on programs. Therefore, the difference between the actual percent (92%) and the prediction (slightly more than 85%) is slightly less than 7%.

Choice A is incorrect. There is no charity represented in the scatterplot for which the difference between the actual percent of total expenses spent on programs and the percent predicted by the line of best fit is as much as 10%. Choices C and D are incorrect. These choices may result from misidentifying in the scatterplot the point that represents the charity with the greatest percent of total expenses spent on programs.

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Two-variable data: Models and scatterplots SAT question

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