AP® Statistics 2007 Scoring Guidelines Form B 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. © 2007 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, SAT, and the acorn logo are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. 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 2007 SCORING GUIDELINES (Form B) © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). Question1 Intent of QuestionThe three primary goals of this question are to assess a student’s ability to: (1) construct a stemplot from a given data set; (2) describe the important features of the plot; and (3) discuss how a single measure of centrality fails to convey important features of the plot. SolutionPart (a): 0| 89 1| 26878993640 2| 3| 3856 4| 143 Legend: 1| 2 represents 12 questions answered correctly OR, with ordered leaves (not required) 0| 89 1| 02346678899 2| 3| 3568 4| 134 Legend: 1| 2 represents 12 questions answered correctly OR, with repeated stems (leaves may be ordered or not) 0H 89 1L 0234 1H 6678899 2 L 2H 3L 3 3H 568 Legend: 3H 6 represents 36 questions answered correctly 4L 134 4L 1 represents 41 questions answered correctly Part (b): The most striking feature of the plot is that the scores cluster into two groups, one concentrated in the mid-teens and the other in the high 30s (or one with relatively low scores on the exam and one with relatively high scores). There are no scores in the 20s. Part (c): A measure of center might fall between the two groups (as does the mean of 22.95 here) where there is no data and would not provide an accurate picture of student performance on the exam. It would not indicate that students tended to score either very well or very poorly on the exam. www.mymathscloud.com
AP® STATISTICS 2007 SCORING GUIDELINES (Form B) © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). Question1 (continued) ScoringThis question is scored in four sections: section 1 is part (a), and sections 2 to 4 consist of elements of parts (b) and (c). Section 1 is scored as either essentially correct (E) or incorrect (I).Section 1is essentially correct (E) if in part (a) the student gives a correctly constructed stemplot. Any other type of plot is incorrect (I). NOTE: One or two misplaced or omitted leaves can still be considered essentially correct as long as the important features of the display are not altered. Parts (b) and (c) are scored together in three sections, each of which is scored as essentially correct (E), partially correct (P), or incorrect (I). Section 2 is essentially correct (E) if in either part (b) or (c) the student clearly notices: 1.that there are two groups; 2.that there is a gap in the middle of the distribution; 3.the relative or specific positions of the two groups, OR the location of the gap, OR a general measure of location (such as mean, median, or the fact that most scores fall between 10 and 19). (Median = 18, mean = 22.95) Section 2 is partially correct (P) if the student notes two out of the three. Section 3 is essentially correct (E) if in part (b) or part (c) the solution is given in the context of the problem and is communicated well. Section 3 is partially correct (P) if the student mentions the context (for instance, using the word “scores”), but communication of the context is weak. Section 3 is incorrect (I) if the context is not mentioned at all. Section 4 is essentially correct (E) if in part (c) a valid reason is given for why a measure of center is not sufficient for data of this type (with the two groups and a gap). If, for instance, the reasoning would apply equally well to other shapes, it is not sufficient. Section 4 can be at most partially correct (P) if a student does not recognize the groups or gap. It is partially correct if the student compares the mean and median and cites outliers or skewness as the reason why a measure of center is not sufficient, or if a general reason is given for why a measure of center is not sufficient. (For instance, the student may say that center alone without some measure of spread is never sufficient.) www.mymathscloud.com
AP® STATISTICS 2007 SCORING GUIDELINES (Form B) © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). Question1 (continued) 4 Complete Response All four sections essentially correct 3 Substantial ResponseThree sections essentially correct and no sections partially correct OR Two sections essentially correct and two sections partially correct 2 Developing ResponseTwo sections essentially correct and no sections partially correct OR One section essentially correct and two sections partially correct Note: A score cannot exceed 2 if (1) the student fails to notice either of the two distinct groups of scores or the gap between the groups, and (2) the response to part (c) mentions neither the two groups nor the gap. 1 Minimal Response One section essentially correct and no sections partially correct OR No sections essentially correct and two sections partially correct If a response is between two scores (for example, 2½ points), use a holistic approach to determine whether to score up or down depending on the strength of the response and communication.www.mymathscloud.com
AP® STATISTICS 2007 SCORING GUIDELINES (Form B) © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). Question2 Intent of QuestionThe three primary goals of this question are to assess a student’s ability to: (1) calculate a probability from a display of population frequencies; (2) calculate a binomial probability; and (3) describe a sampling distribution of a sample mean for a moderately large sample. SolutionPart (a): ()> 30.070.040.040.020.17.PX=+++=Part (b): Y = number of households in violation. Y has a binomial distribution with 10n= and 0.17.p=2810(2)(0.17) (0.83)0.2929.2PY⎛⎞===⎜⎟⎝⎠Part (c): The distribution of X will: 1.be approximately normal; 2.have mean 1.65;Xμμ==3.have standard deviation 1.8510.1511.150Xnσσ== =Scoring This question is scored in four sections. Each section is scored as either essentially correct (E), partially correct (P), or incorrect (I). Section 1 is part (a), section 2 is part (b), and sections 3 and 4 consist of elements of part (c). This scoring gives part (c) double weight relative to either part (a) or part (b).Section 1 is essentially correct (E) if ()3PX>is correctly computed and work is shown in part (a). Section 1 is partially correct (P) if: ()30.26PX≥= is computed; OR a correct numerical answer is given but no work is shown. www.mymathscloud.com
