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Question 3 of 30

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M:C:MC:SET:2A

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SAT

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PSAT/NMSQT

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PSAT 10

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Problem Solving and Data Analysis

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Questions 3–5 refer to the following information.

The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown.

The figure presents a graph of a scatterplot titled “Height of Nine People and Length of Their First Metacarpal Bone,” and a line. The horizontal axis is labeled “Length of first metacarpal bone,” in centimeters, and the vertical axis is labeled “Height,” in centimeters.  There are equally spaced horizontal gridlines labeled, from bottom to top, 155 through 185, in increments of 5. There are equally spaced vertical gridlines labeled, from left to right, 4 through 5, in increments of zero point five. A straight line of best fit starts on the leftmost vertical axis at 4 comma 161.5 and stops at the intersection of the rightmost vertical gridline at 5 comma 180. There are 9 data points in the graph. From left to right, the coordinates are as follows: First point: 4 comma 157, Second point: 4.1 comma 163, Third point: 4.3 comma 175, Fourth point: 4.5 comma 171, Fifth point: 4.6 comma 173, Sixth point: 4.7 comma 173, Seventh point: 4.8 comma 172, Eighth point: 4.9 comma 183, and Ninth point: 5 comma 178

How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

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2

Correct Answer: 
No

4

Correct Answer: 
Yes

6

Correct Answer: 
No

9

Correct Answer: 
No

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Choice B is correct. The people who have first metacarpal bones of length 4.0, 4.3, 4.8, and 4.9 centimeters have heights that are greater than 3 centimeters different from the height predicted by the line of best fit.

Choice A is not the correct answer. There are 2 people whose actual heights are more than 3 centimeters above the height predicted by the line of best fit. However, there are also 2 people whose actual heights are farther than 3 centimeters below the line of best fit.

Choice C is not the correct answer. There are 6 data points in which the absolute value of the between the actual height and the height predicted by the line of best fit is greater than 1 centimeter.

Choice D is not the correct answer. The data on the graph represents 9 different people; however, the absolute value of the difference between actual height and predicted height is not greater than 3 for all of the people.

Question Difficulty: 
easy
Objective: 

Students must read and interpret information from a data display.