Question #1

Scoring 4Complete 3Substantial 2Developing 1Minimal 0

The primary goals of this question were to assess a student's ability to (1)compare features of two distributions of data displayed in boxplots and (2) recognize that a graphical display of the differences for paired data can provide additional information not present in graphical displays of the data from each of the two samples. Intent of Question

Question #1 Students in an AP Statistics class participated in an online memory game. All of the students first played the game at Level 1 (the lowest difficulty level), and then played the game again at Level 4 (a higher level of difficulty). The graphs below display the distribution of student scores for the two difficulty levels – Level 1 and Level 4. a) Use the graphical display above to compare the distribution of student scores for the two difficulty levels (Level 1 and Level 4) of the memory game.

Solution Part (a): Students tended to score higher on Level 1 than on Level 4 of the memory game, as the median score for the students in this class on Level 1 of the memory game was almost twice as high as the Level 4 score. In fact, all but one of the Level 4 scores was below the first quartile of scores for Level 1. There was more variability in the Level 1 scores, with both the IQR and range being almost twice that of Level 4. The shapes of the distributions differ, in that the distribution of scores for Level 1 of the memory game is fairly symmetric with perhaps a slight skew to the left while the distribution of the Level 4 scores is right skewed with a high outlier of about 700 points.

Scoring Parts (a) is scored as essentially correct (E), partially correct (P), or incorrect (I). Part (a) is scored as follows: Essentially correct (E) if the response includes the following four components : 1)A correct comparison of center. 2)A correct comparison of spread. 3)A correct description of the skewness of the two distributions and the outlier in the Level 4 distribution. 4) The response is in context. Partially correct (P) if the response includes only three of the four components listed above. Incorrect (I) if the response includes at most two of the four components listed above. Note : Any mention of the modality of the two distributions should be ignored because the modality of a distribution cannot be determined from a boxplot.

Question #1 continued The difference in scores (Level 4 – Level 1) on the memory game was calculated for each student. The graph below displays the distribution of the differences. b) What added information does the graph above of the difference in scores (Level 4 – Level 1) give you about students' scores on the two different levels of the game that was not apparent in the first graphical display?

Solution Part (b): The graph of the differences in scores (Level 4 – Level 1) is entirely below zero revealing that all students scored higher on Level 1 of the game than on Level 4 of the memory game, by approximately 100 to 1000 points higher. This information is not available in the first graphical display because the scores for Level 1 are not paired with the scores on Level 4 for the same player.

Scoring Parts (b) is scored as essentially correct (E), partially correct (P), or incorrect (I). Part (b) is scored as follows: Essentially correct (E) if the response includes the following three components: 1)A correct aspect of the graph of the differences not apparent in the first graphical display (all of the students scored higher on Level 1 than on Level 4, the range of the differences in individual students' scores) is given. 2)An explanation of why the aspect mentioned in component 1 cannot be seen in the first graphical display. 3)The response is in context. Partially correct (P) if the response includes component 1 and either component 2 or 3 but not both. Incorrect (I) if the response does not meet the criteria for E or P.

Question #1 Scoring 4Complete Response Both parts essentially correct 3Substantial Response One part essentially correct and one part partially correct 2Developing Response One part essentially correct and one or part incorrect OR Both parts partially correct 1Minimal Response One part partially correct one part incorrect