1. **Stating the problem:** We are given a box and whisker diagram representing the number of sick days taken by employees in a year. We need to identify the minimum, lower quartile, and median from the diagram and analyze a claim about the distribution of sick days. 2. **Understanding the box and whisker diagram:** - The minimum is the smallest value (left whisker end). - The lower quartile (Q1) is the left edge of the box. - The median (Q2) is the line inside the box. - The upper quartile (Q3) is the right edge of the box. - The maximum is the right whisker end. 3. **From the diagram:** - Minimum number of sick days = 2 (left whisker end). - Lower quartile (Q1) = 6 (left edge of the box). - Median (Q2) = 11 (line inside the box). 4. **Answering part (a):** (a.i) Minimum number of sick days = $2$ (a.ii) Lower quartile = $6$ (a.iii) Median = $11$ 5. **Analyzing part (b):** Paul claims: "The percentage of employees who took fewer than 6 sick days is smaller than the percentage who took more than 11 sick days." - The lower quartile $Q1=6$ means 25% of employees took fewer than 6 sick days. - The median $Q2=11$ means 50% took fewer than 11 sick days, so 50% took more than 11 sick days. Therefore: - Percentage with fewer than 6 sick days = 25% - Percentage with more than 11 sick days = 50% Paul's claim is correct because 25% < 50%. **Final answers:** - (a.i) Minimum = $2$ - (a.ii) Lower quartile = $6$ - (a.iii) Median = $11$ - (b) Paul is correct; fewer than 6 sick days corresponds to 25% of employees, which is less than the 50% who took more than 11 sick days.