Find the 5 number summary for the data shown \begin{tabular}{|c|c|} \hline 6 & 10 \\ \hline 12 & 13 \\ \hline 19 & 38 \\ \hline 46 & 51 \\ \hline 55 & 67 \\ \hline 87 & \\ \hline \end{tabular} 5 number summary: Use the Locator/Percentile method described in your book, not your calculator:
Solution
Step 1 ：First, we need to sort the data in ascending order. The data given is [6, 10, 12, 13, 19, 38, 46, 51, 55, 67, 87].
Step 2 ：The minimum value of the data set is the smallest number, which is \(6\).
Step 3 ：The first quartile (Q1) is the median of the lower half of the data. In this case, Q1 is \(12.5\).
Step 4 ：The median (Q2) is the middle number of the data set. If the data set has an even number of observations, the median is the average of the two middle numbers. In this case, the median is \(38\).
Step 5 ：The third quartile (Q3) is the median of the upper half of the data. In this case, Q3 is \(53\).
Step 6 ：The maximum value of the data set is the largest number, which is \(87\).
Step 7 ：So, the 5 number summary for the given data is \(\boxed{(6, 12.5, 38, 53, 87)}\).
