In the data set below, what is the lower quartile? \( \begin{array}{llllll}1 & 1 & 2 & 5 & 7 & 8\end{array} \)

To find the lower quartile (Q1), first, order the data set, which is already sorted: \(1, 1, 2, 5, 7, 8\). Since there are 6 data points, the lower quartile is the median of the first half of the data. The first half is \(1, 1, 2\). The median of this half is the second value, which is \(1\). Therefore, the lower quartile is \(1\). Another way to think about quartiles is that they split the sorted data into four equal parts. The lower quartile represents the value below which 25% of the data points fall. In this case, with most of the numbers clustered around 1, it’s easy to see why the lower quartile would reflect that, making it intuitive as well as mathematically precise!