Sixth grade \( \quad 31.7 \) Calculate quartiles and interquartile range MNV In the data set below, what is the upper quartile? \( \begin{array}{lllllll}59 & 59 & 60 & 66 & 68 & 68 & 72\end{array} 73 \)

To find the upper quartile (Q3) of the given data set \(59, 59, 60, 66, 68, 68, 72, 73\), we first arrange the numbers in ascending order (already done here). The upper quartile is the median of the upper half of the data. The median position is found by taking the average of the 4th and 5th numbers: \(66\) and \(68\), which means the median (Q2) is \(67\). For Q3, consider the upper half: \(68, 72, 73\). The median of these numbers is \(72\), which is our upper quartile. The interquartile range (IQR) is then calculated as \(Q3 - Q1\). First, we find Q1, which is the median of the lower half \(59, 59, 60, 66\). The median here is the average of the 2nd and 3rd terms: \(59\) and \(60\), yielding \(59.5\) for Q1. Therefore, the IQR is \(72 - 59.5 = 12.5\). So, the upper quartile is \(72\) and the interquartile range is \(12.5\).