Date | May 2022 | Marks available | 3 | Reference code | 22M.1.SL.TZ2.7 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 2 |
Command term | Show that | Question number | 7 | Adapted from | N/A |
Question
A college runs a mathematics course in the morning. Scores for a test from this class are shown below.
For these data, the lower quartile is and the upper quartile is .
The box and whisker diagram showing these scores is given below.
Test scores
Another mathematics class is run by the college during the evening. A box and whisker diagram showing the scores from this class for the same test is given below.
Test scores
A researcher reviews the box and whisker diagrams and believes that the evening class performed better than the morning class.
Show that the test score of would not be considered an outlier.
With reference to the box and whisker diagrams, state one aspect that may support the researcher’s opinion and one aspect that may counter it.
Markscheme
OR seen anywhere OR seen anywhere (M1)
A1
R1
so is not an outlier AG
[3 marks]
The median score for the evening class is higher than the median score for the morning class. A1
THEN
but the scores are more spread out in the evening class than in the morning class A1
OR
the scores are more inconsistent in the evening class A1
OR
the lowest scores are in the evening class A1
OR
the interquartile range is lower in the morning class A1
OR
the lower quartile is lower in the evening class A1
Note: If an incorrect comparison is also made, award at most A1A0.
Award A0 for a comparison that references “the mean score” unless working is shown for the estimated means of the data sets, calculated from the mid-points of the 4 intervals. The estimated mean for the morning class is and the estimated mean for the evening class is .
[2 marks]
Examiners report
There were mixed results calculating the boundary value for outliers. Some determined the correct value of 23, but did not relate it back to 25. Some did not realize that a calculation had to be performed, and instead tried to present an argument referencing the box and whisker diagram.
The majority of candidates were able to compare the medians as evidence supporting the researcher’s belief. However, some incorrectly referred to the median values as mean values. There were more counterarguments available to be presented, and again, candidates were generally able to communicate one of these. There were occasions where the candidate did not indicate which argument was in support of the researcher and which argument was the counterargument, which is an important element in the labelling/communication of their response.