2004 AP Statistics Scoring Guidelines - College Board

1 AP Statistics2004 Scoring Guidelines 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 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three 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.

2 For further information, visit Copyright 2004 College Entrance Examination Board . All rights reserved. College Board , Advanced Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of the College Entrance Examination Board . PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service. Other products and services may be trademarks of their respective owners. For the College Board s online home for AP professionals, visit AP Central at The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must be sought from the Advanced Placement Program.

3 Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. This permission does not apply to any third-party copyrights contained herein. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. AP Statistics 2004 Scoring Guidelines Copyright 2004 by College Entrance Examination Board . All rights reserved. Visit (for AP professionals) and (for AP students and parents). 2 Question 1 Solution Part (a): Additive A Additive B IQR 41 3 = ()25227 = *IQR IQRQ = 2 = IQRQ+ 4 + = 25 + = 3 outliers no outliers Part (b i): Additive A is better at increasing the mileage in the greatest number of cars.

4 The mileage increased for at least seventy-five percent of the cars with additive A, whereas the mileage decreased for more than twenty-five percent of the cars with additive B. Part (b ii): Additive B appears to produce a higher mean mileage gain than additive A. The boxplot for additive B clearly shows that the distribution of differences is skewed to the right, which will pull the average towards the larger values. The mean difference for additive B will be substantially greater than the median of 1. On the other hand, the distribution of differences for additive A has much less variability, as seen by comparing the lengths of the two boxes, and appears to be skewed to the left. The mean difference for additive A will be less than the median of 3. AP Statistics 2004 Scoring Guidelines Copyright 2004 by College Entrance Examination Board .

5 All rights reserved. Visit (for AP professionals) and (for AP students and parents). 3 Question 1 (cont d.) Scoring Each part is scored as essentially correct, partially correct, or incorrect. Part (a) is essentially correct if parallel boxplots are correctly drawn and the display includes labels. The labels for additives A and B are required, but if the label for either axis (or both axes) is the only item missing then part (a) is still scored as essentially correct. Part (a) is partially correct if only one of the following occurs: if neither additive A nor B is labeled, or the labels are reversed, OR there is an error in the construction of the boxplots, OR outliers are not correct, but otherwise the boxplots are correct. Note: If the same error is present in the boxplot for Additive A as in the boxplot for Additive B, count this as one error, not two.

6 Part (a) is incorrect if either of the following occur: 2 or 3 of the errors above are committed OR the numbers provided in the stem of the problem are used as a data set to form the boxplots below. INCORRECT BOXPLOTS USING SUMMARY Statistics AS DATA Note: If the labeling is reversed for boxplots A and B, score parts (b i) and (b ii) consistently with the reversed labels. AP Statistics 2004 Scoring Guidelines Copyright 2004 by College Entrance Examination Board . All rights reserved. Visit (for AP professionals) and (for AP students and parents). 4 Question 1 (cont d.) Part (b i) is essentially correct if additive A is selected as the additive that will increase the mileage in the greatest number of cars and the explanation involves a comparison implicitly or explicitly using the first quartiles from both distributions. Part (b i) is partially correct if any of the following occur: additive A is selected, but the only comparison is between the lower quartile of additive A and the median of additive B, OR additive A is selected as the additive that will increase the mileage in the greatest number of cars but the comparison is weak or incomplete, such as relying only on variability or only on the median, OR additive A is selected and justified by addressing either A or B, but there is no explicit comparison to the other additive.

7 Part (b i) is scored as incorrect if any of the following occur: additive A is selected, but no explanation is provided, OR additive A is selected, but the explanation is incorrect, OR additive B is selected, OR summary Statistics are used correctly in part (a), but used as data in part (b). Part (b ii) is essentially correct if additive B is selected as the additive that will produce a higher mean mileage gain and the explanation involves a comparison using the shapes of both distributions. For additive A it is sufficient to refer to the effect of the outliers on the mean. Part (b ii) is partially correct if any of the following occur: additive B is selected as the additive that will produce a higher mean mileage gain but the comparison is weak or incomplete, OR additive B is selected and justified by addressing either A or B, but there is no explicit comparison to the other additive, OR additive A is selected, because the student argues that medians should be used to measure center instead of means because of the outliers or because the distributions are skewed, OR a comparison is made between A and B, but only one side, either left or right, is addressed for both plots.

8 Part (b ii) is scored as incorrect if any of the following occur: additive B is selected, but no explanation is provided, additive B is selected, but the explanation is incorrect, additive A is selected for any reason other than that stated above for partially correct, summary Statistics are used correctly in part (a), but used as data in part (b), OR the student claims that the means cannot be determined from the information provided. AP Statistics 2004 Scoring Guidelines Copyright 2004 by College Entrance Examination Board . All rights reserved. Visit (for AP professionals) and (for AP students and parents). 5 Question 1 (cont d.) 4 Complete Response All three parts essentially correct 3 Substantial Response Two parts essentially correct and 1 part partially correct 2 Developing Response 2 parts essentially correct and no parts partially correct OR One part essentially correct and 2 parts partially correct OR 3 parts partially correct 1 Minimal Response One part essentially correct and either 0 or 1 part partially correct OR No parts essentially correct and 2 parts partially correct AP Statistics 2004 Scoring Guidelines Copyright 2004 by College Entrance Examination Board .

9 All rights reserved. Visit (for AP professionals) and (for AP students and parents). 6 Question 2 Solution Part (a): Block Volunteers Ages 1 1, 2 20, 21 2 10, 11 23, 24 3 8, 9 44, 44 4 3, 12 46, 47 5 4, 7 58, 60 6 5, 6 61, 62 Since these researchers believe that the condition of hair changes with age but not gender, the volunteers are sorted from youngest to oldest. The volunteers in the sorted list are paired to form six blocks of size two. More specifically, the youngest two volunteers are placed in the first block. The next two volunteers in the sorted list are placed in the second block. This pairing continues until all six blocks of two are formed, with the oldest two volunteers in the sixth block. Part (b): Block Volunteers Ages Female 1 2, 10 20, 24 Female 2 8, 12 44, 46 Female 3 4, 5 60, 62 Male 1 1, 11 21, 23 Male 2 3, 9 47, 44 Male 3 6, 7 61, 58 Since these researchers believe that the condition of hair changes with both age and gender, the women are sorted from youngest to oldest and then the men are sorted from youngest to oldest.

10 The women (men) in the sorted list are paired to form the blocks of size two. More specifically, the youngest two women (men) are placed in a block. The next two youngest women (men) are placed in another block. Finally, the oldest two women (men) are placed in another block. Part (c): No, the researchers in part (b) should not randomly select three blocks to receive the new formula and then give the current formula to the other three blocks. They blocked on both age and gender to form homogeneous groups because they believe hair condition differs with both age and gender. Giving the youngest or oldest women (men) the same formula defeats the purpose of blocking. In a block design, randomization should be carried out separately within each block. That is, for each block, two random numbers are generated (via a random number generator or a table of random digits) and assigned to the two volunteers.