| Date | May 2015 | Marks available | 2 | Reference code | 15M.1.sl.TZ1.2 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
The IB grades attained by a group of students are listed as follows.
\[{\text{6}}\;\;\;{\text{4}}\;\;\;{\text{5}}\;\;\;{\text{3}}\;\;\;{\text{7}}\;\;\;{\text{3}}\;\;\;{\text{5}}\;\;\;{\text{4}}\;\;\;{\text{2}}\;\;\;{\text{5}}\]
Find the median grade.
Calculate the interquartile range.
Find the probability that a student chosen at random from the group scored at least a grade \(4\).
Markscheme
\(2\;\;\;3\;\;\;3\;\;\;4\;\;\;4\;\;\;5\;\;\;5\;\;\;5\;\;\;6\;\;\;7\) (M1)
Note: Award (M1) for correct ordered set.
\(({\text{Median}} = ){\text{ }}4.5\) (A1) (C2)
\(5 - 3\) (M1)
Note: Award (M1) for correct quartiles seen.
\( = 2\) (A1) (C2)
\(\frac{7}{{10}}\;\;\;(0.7,{\text{ }}70\% )\) (A2) (C2)
Examiners report
Part (a) was generally well done although some candidates seemed to be confused between the mean and median.
In part (b) it was not unusual to see an upper quartile of 5.5 (resulting from (5+6)/2).
A significant number of candidates had difficulty with “at least four” in part (c), answering 2/10 which resulted from calculating the probability of a grade equal to 4 and not at least 4.
