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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 “Density of Grape Juice.” The horizontal axis is labeled “Concentration,” and the percents 20 percent through 80 percent, in increments of 10 percent, are indicated. The vertical axis is labeled “Density, in kilograms per cubic meter,” and the numbers 1,000 through 1,400, in increments of 50, are indicated. There are 10 data points that begin in the lower left part of the scatterplot and trend upward and to the right. The data represented by the points are as follows. Note that all values are approximate. Concentration, 23 percent. Density, 1,100 kilograms per cubic meter. Concentration, 27 percent. Density, 1,110 kilograms per cubic meter. Concentration, 32 percent. Density, 1,125 kilograms per cubic meter. Concentration, 35 percent. Density, 1,150 kilograms per cubic meter. Concentration, 42 percent. Density, 1,190 kilograms per cubic meter. Concentration, 45 percent. Density, 1,210 kilograms per cubic meter. Concentration, 51 percent. Density, 1,240 kilograms per cubic meter. Concentration, 54 percent. Density, 1,260 kilograms per cubic meter. Concentration, 67 percent. Density, 1,345 kilograms per cubic meter. Concentration, 71 percent. Density, 1,360 kilograms per cubic meter.

The densities of different concentrations of grape juice are shown in the scatterplot above. According to the trend shown by the data, which of the following is closest to the predicted density, in kilograms per cubic meter (kg/m3), for grape juice with a concentration of 60%?

ExplanationShow

Choice C is correct. The data in the scatterplot show an increasing linear trend. The density when the juice concentration is 60% will be between the densities shown at about 53% and 67% concentration, or between about 1,255 and 1,340 kg/m3. Of the choices given, only 1,300 falls within this range.

Choices A, B, and D are incorrect. These are the approximate densities of grape juice with a concentration of 45%, 55%, and 70%, respectively.

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