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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 line graph titled “Number of 3 D Movies Released by Year.” The horizontal axis is labeled “Year,” and the years 2003 through 2011 are indicated. The vertical axis is labeled “Number of 3 D movies released,” and the numbers 0 through 50, in increments of 10, are indicated. The data, represented by 9 points on the graph, are as follows. Note that all values are approximate. 2003, 2 movies. 2004, 2 movies. 2005, 6 movies. 2006, 8 movies. 2007, 6 movies. 2008, 8 movies. 2009, 20 movies. 2010, 26 movies. 2011, 46 movies.

According to the line graph above, between which two consecutive years was there the greatest change in the number of 3‑D movies released?

ExplanationShow

Choice D is correct. The change in the number of 3-D movies released between any two consecutive years can be found by first estimating the number of 3-D movies released for each of the two years and then finding the positive difference between these two estimates. Between 2003 and 2004, this change is approximately 2 minus 2, equals 0 movies; between 2008 and 2009, this change is approximately 20 minus 8, equals 12 movies; between 2009 and 2010, this change is approximately 26 minus 20, equals 6 movies; and between 2010 and 2011, this change is approximately 46 minus 26, equals 20 movies. Therefore, of the pairs of consecutive years in the choices, the greatest increase in the number of 3-D movies released occurred during the time period between 2010 and 2011.

Choices A, B, and C are incorrect. Between 2010 and 2011, approximately 20 more 3-D movies were released. The change in the number of 3-D movies released between any of the other pairs of consecutive years is significantly smaller than 20.

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