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Two-variable data: Models and scatterplots SAT question

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

The figure presents a scatterplot titled “Distance and Density of Planetoids in the Inner Solar System.” The horizontal axis is labeled “Distance from the Sun,” in astronomical units (A U), and the numbers zero through 3 point 2, in increments of zero point 4, are indicated. The vertical axis is labeled “Density,” in grams per cubic centimeter, and the numbers 3 through 6, in increments of zero point 5, are indicated. The graph has 7 data points. Three of the points are grouped in the upper left corner of the graph, below 1 point 2 A U and above 5 grams per cubic centimeter. The remaining points are above 1 point 4 A U and below 4 grams per cubic centimeter, with 3 of the points grouped in the lower right corner above 2 point 2 A U and below 3 point 7 5 grams per cubic centimeter. The line of best fit is also graphed. The line of best fit passes through the following coordinates on the grid. All data are approximate: zero A U, 5 point 7 5 grams per cubic centimeter. Zero point 8 A U; 5 grams per cubic centimeter. 1 point 6 A U; 4 point 2 5 grams per cubic centimeter. 2 point 4 A U; 3 point 5 grams per cubic centimeter. 2 point 9 A U; 3 grams per cubic centimeter.

The scatterplot above shows the densities of 7 planetoids, in grams per cubic centimeter, with respect to their average distances from the Sun in astronomical units (AU). The line of best fit is also shown. An astronomer has discovered a new planetoid about 1.2 AU from the Sun. According to the line of best fit, which of the following best approximates the density of the planetoid, in grams per cubic centimeter?

ExplanationShow

Choice C is correct. According to the line of best fit, a planetoid with a distance from the Sun of 1.2 AU has a predicted density between 4 point 5 grams per cubic centimeter and 4 point 7 5 grams per cubic centimeter. The only choice in this range is 4.6.

Choices A, B, and D are incorrect and may result from misreading the information in the scatterplot.

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