IB Mathematics SL 4.2 Presentation of data AI SL Paper 1- Exam Style Questions- New Syllabus
Question
The number of sick days taken by each employee in a company during a year was recorded. The data was organized in a box and whisker diagram as shown below:

For this data:
(a)(i) State the minimum number of sick days taken during the year. [1]
(a)(ii) State the lower quartile. [1]
(a)(iii) State the median. [1]
(b) Jordan claims that this box and whisker diagram can be used to infer that the percentage of employees who took fewer than six sick days is smaller than the percentage of employees who took more than eleven sick days. Determine whether Jordan is correct. Justify your answer. [2]
▶️ Answer/Explanation
Markscheme
(a)(i)
Minimum value (leftmost whisker): 2 sick days. A1
[1 mark]
Minimum value (leftmost whisker): 2 sick days. A1
[1 mark]
(a)(ii)
Lower quartile (\( Q_1 \), left edge of box): 6 sick days. A1
[1 mark]
Lower quartile (\( Q_1 \), left edge of box): 6 sick days. A1
[1 mark]
(a)(iii)
Median (\( Q_2 \), line inside box): 8 sick days. A1
[1 mark]
Median (\( Q_2 \), line inside box): 8 sick days. A1
[1 mark]
(b)
Jordan is not correct. A1
From the diagram: minimum = 2, \( Q_1 = 6 \), median = 8, assume \( Q_3 = 11 \), maximum = 14 (inferred). Employees with fewer than 6 sick days (below \( Q_1 \)) are approximately 25%. Employees with more than 11 sick days (above \( Q_3 \)) are also approximately 25%. Since both are roughly equal, the claim is incorrect. Alternatively, the diagram lacks precise data for exact percentages at 6 and 11, and discrete data complicates the inference. M1
[2 marks]
Jordan is not correct. A1
From the diagram: minimum = 2, \( Q_1 = 6 \), median = 8, assume \( Q_3 = 11 \), maximum = 14 (inferred). Employees with fewer than 6 sick days (below \( Q_1 \)) are approximately 25%. Employees with more than 11 sick days (above \( Q_3 \)) are also approximately 25%. Since both are roughly equal, the claim is incorrect. Alternatively, the diagram lacks precise data for exact percentages at 6 and 11, and discrete data complicates the inference. M1
[2 marks]
Total Marks: 5