Transcript Q1.pptx

Question #1
Scoring
4 Complete
3 Substantial
2 Developing
1 Minimal
0
Intent of Question
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.
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
4
Complete Response
Both parts essentially correct
3
Substantial Response
One part essentially correct and one part partially correct
2
Developing Response
OR
1
One part essentially correct and one or part incorrect
Both parts partially correct
Minimal Response
One part partially correct one part incorrect