(a) The minimum number of overtime hours worked is correctly identified from the box-and-whisker plot. This value is 2 hours of overtime.

(b)(i) The lower quartile is correctly identified from the box-and-whisker plot. This is a value of 6 hours of overtime. It means that 25% of the data is below this value and 75% is above.

(b)(ii) The median is correctly identified from the box-and-whisker plot. This is a value of 8 hours of overtime. It can be identified as the vertical line contained within the box and means that 50% of the data will be above this value and 50% will be below. In other words, it is the middle value of the data when all data points are put in order.

(c) A clear statement is made as to whether the claim is valid, supported by correct reasoning based on the interquartile range (IQR) and/or proportions of data. The IQR is calculated by subtracting the lower quartile \(Q_1\) from the upper quartile \(Q_3\): \( \text{IQR} = Q_3 – Q_1 \). We can see that in this instance it is possible that 20% of employees worked less than 5 overtime hours since 5 is below \( Q_2 \). But it does not make sense that 30% worked more than 15 hours since we know that the upper quartile is at 11, which means only 25% of the data can be contained above that.