AP® Statistics 2006 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 5,000 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. © 2006 The College Board. All rights reserved. College Board, AP Central, APCD, Advanced Placement Program, AP, AP Vertical Teams, Pre-AP, SAT, and the acorn logo are registered trademarks of the College Board. Admitted Class Evaluation Service, CollegeEd, connect to college success, MyRoad, SAT Professional Development, SAT Readiness Program, and Setting the Cornerstones are trademarks owned by the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program: apcentral.collegeboard.com. www.mymathscloud.com
AP® STATISTICS 2006 SCORING GUIDELINES © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 2 Question 1 Intent of QuestionThe primary goals of this question are: (1) to assess a student’s ability to use simple graphical displays (dotplots in this case) to compare and contrast two distributions; and (2) to evaluate a student’s ability to recognize what statistical information is most useful in making different practical decisions. SolutionPart (a): Both distributions of distances are roughly symmetric and somewhat mound-shaped. The center of the distances for catapult A (median A = 136 cm) is slightly lower than the center of the distances for catapult B (median B = 138 cm). There is more variability in the distances traveled by the Ping-Pong balls launched with catapult A. There are distances that are extreme enough to be called (potential) outliers in the catapult A distribution, but there are no outliers among the catapult B distances. Part (b): Catapult B would be best because the distances vary less about the center of the distribution for catapult B. If catapult B is properly placed, the balls launched will have a higher probability of landing in the narrow (only 5 cm wide) target band. Part (c): The catapult should be placed 138 cm from the target line. Since the distribution of distances for catapult B seems to be fairly symmetric and somewhat mound-shaped, the median (138 cm) is a good representation of the center of the distribution. Placing catapult B at this location would have resulted in a high proportion (30/40 = 0.75) of Ping-Pong balls from this sample of launches landing in the target band. ScoringParts (a), (b), and (c) are scored as essentially correct (E), partially correct (P), or incorrect (I). Part (a) is essentially correct (E) if the student correctly identifies similarities and differences in center, spread, and shape for the two distributions. Part (a) is partially correct (P) if the student correctly identifies similarities and differences in two of the three characteristics (center, shape, and spread) for the two distributions. Part (a) is incorrect (I) if the student correctly identifies no more than one similarity or difference of the three characteristics (center, shape, and spread) for the two distributions. Notes: •Correct comments regarding outliers should be viewed as a positive. However, comments about outliers do not count as one of the three required characteristics. www.mymathscloud.com
AP® STATISTICS 2006 SCORING GUIDELINES © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 3 Question 1 (continued) •Describing catapult A’s distribution as “normal” or “skewed left” or “uniform” is not acceptable for the shape characteristic. Describing either distribution as “approximately normal” is acceptable. •Giving separate lists of measures of center and/or spread for the two distributions with no linkage between them is not an acceptable discussion of similarities and differences for these characteristics. Part (b) is essentially correct (E) if catapult B is chosen using a rationale based on the variability in the distances. Part (b) is partially correct (P) if catapult B is chosen, but the explanation does not refer to the variability in the distances. Part (b) is incorrect (I) if catapult B is chosen and no explanation is provided OR catapult A is chosen. Part (c) is essentially correct (E) if:the catapult is placed at the median (or mean) of the distances traveled by the Ping-Pong balls, and the explanation addresses why the median (or mean) was selected based on a property of the chosen statistic that relates to the context of the problem; OR the catapult is placed at a distance of 137.5-139.5 cm from the target line, and the explanation indicates that the chosen distance resulted in a high proportion of the balls in the sample landing in the target band. Part (c) is partially correct (P) if the catapult is placed at an acceptable distance from the target line, but the explanation is incomplete or incorrect. Part (c) is incorrect (I)if the catapult is placed less than 137.5 centimeters or more than 139.5 centimeters from the target line. Notes: •Simply saying “because it’s the median (or mean)” is an incomplete explanation. •Some students may confuse the 5 cm band as meaning 5 cm on either side of the target line. If the student chooses the median (or mean) and satisfactorily addresses why the median (or mean) was selected OR chooses a value of 137-140 cm and the explanation indicates that the chosen distance resulted in a high proportion of the balls in the sample landing in the target band, score the response as partially correct. •If a student gives the distance from the catapult to the front or back of the shaded band rather than the distance to the target line, but gives an otherwise correct response, score part (c) as partially correct. •If a student picks catapult A in part (b) and follows through correctly in part (c), then part (c) should be scored as essentially correct. www.mymathscloud.com
AP® STATISTICS 2006 SCORING GUIDELINES © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 4 Question 1 (continued) 4 Complete Response All three parts essentially correct 3 Substantial Response Two parts essentially correct and one part partially correct 2 Developing Response Two parts essentially correct and no parts partially correct OR One part essentially correct and two parts partially correct OR Three parts partially correct 1 Minimal Response One part essentially correct and either zero or one part partially correct OR No parts essentially correct and two parts partially correct www.mymathscloud.com
