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Question 5 of 30

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M:C:MC:SET:2C

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SAT

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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

Based on the line of best fit, what is the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters?

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168 centimeters

Correct Answer: 
No

169 centimeters

Correct Answer: 
No

170 centimeters

Correct Answer: 
Yes

171 centimeters

Correct Answer: 
No

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Choice C is correct. Students must see that the scale of the x-axis is 0.1, and therefore the x-value of 4.45 is halfway between the unmarked value of 4.4 and the marked value of 4.5. The student must then find the y-value on the line of best fit that corresponds with an x-value of 4.45, which is 170.

Choice A is not the correct answer. A student who mistakenly finds the point on the line between the x-values of 4.3 and 4.4 will find a predicted metacarpal bone length of 168 centimeters.

Choice B is not the correct answer. A student who mistakenly finds the point on the line that corresponds with an x-value of 4.4 centimeters will find a predicted height of approximately 169 centimeters.

Choice D is not the correct answer. A student who mistakenly finds the point on the line that corresponds with an x-value of 4.5 centimeters will find a predicted height of approximately 171 centimeters. Students might also choose this option if they mistakenly use the data point that has an x-value closest to 4.45 cm.

Question Difficulty: 
easy
Objective: 

Students must use the line of best fit to make a prediction. Students must also demonstrate fluency in reading graphs and decimal numbers.