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M:C:MC:16

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PSAT 10

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Problem Solving and Data Analysis

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The figure presents the graph of a scatterplot with a line, titled "Count of Manatees." The horizontal axis is labeled "Year" and the vertical axis is labeled "Number of Manatees." The years 1990 through 2015 are labeled on the horizontal axis, in increments of 5 years. The numbers 1,000 through 6,000 are labeled on the vertical axis, in increments of 1,000. The line begins at year 1991 with approximately 1,200 manatees and ends at year 2011 with approximately 4,200 manatees. The approximate number of manatees given by the line for the labeled year are as follows: Year: 1995, 1,800 manatees; Year: 2000, 2,600 manatees; Year: 2005, 3,300 manatees; and Year: 2010, 4,100 manatees. There are 24 data points scattered along the line and most of them are between years 1995 through 2005 with the numbers of manatees between 1,400 and 3,200.

The scatterplot above shows counts of Florida manatees, a type of sea mammal, from 1991 to 2011. Based on the line of best fit to the data shown, which of the following values is closest to the average yearly increase in the number of manatees?

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0.75

Correct Answer: 
No

75

Correct Answer: 
No

150

Correct Answer: 
Yes

750

Correct Answer: 
No

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Choice C is correct. The slope of the line of best fit is the value of the average increase in manatees per year. Using approximate values found along the line of best fit (1,200 manatees in 1991 and 4,200 manatees in 2011), the approximate slope can be calculated as fraction numerator 3 comma 000 over denominator 20 end fraction space equals space 150.

Choice A is not the correct answer. This value may result from disregarding the actual scale when approximating the slope and interpreting the scale as if each square represents one unit.

Choice B is not the correct answer. This value may result from disregarding the actual scale when approximating the slope, and interpreting the scale as if each square along the x-axis represents one year and each tick mark along the y-axis represents 100 manatees.

Choice D is not the correct answer. This value may result from disregarding the actual scale along the x-axis when approximating the slope and interpreting each square along the x-axis as one year.

Question Difficulty: 
medium
Objective: 

Students must interpret the slope of the line of best fit for the scatterplot as the average increase in the number of manatees per year, while taking the scales of the axes into consideration.