Problem

Hazardous waste: Following is a list of the number of hazardous waste sites in a sample of states of the United States in a recent year. The list has been sorted into numerical order. \begin{tabular}{llllllllll} \hline 0 & 2 & 3 & 6 & 9 & 9 & 9 & 12 & 12 & 13 \\ 13 & 14 & 14 & 15 & 15 & 15 & 15 & 16 & 16 & 19 \\ 20 & 21 & 25 & 26 & 29 & 30 & 32 & 38 & 97 & 116 \\ \hline Source: U.S. Environmental Protection Agency \end{tabular} Send data to Excel Part: $0 / 4$ Part 1 of 4 (a) Find the first and third quartiles of these data. The first quartile of these data is $\square$. The third quartile of these data is $\square$.

Solution

Step 1 :Given the data set of the number of hazardous waste sites in a sample of states of the United States in a recent year: 0, 2, 3, 6, 9, 9, 9, 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 19, 20, 21, 25, 26, 29, 30, 32, 38, 97, 116.

Step 2 :The first quartile (Q1) is the middle number between the smallest number and the median of the data set.

Step 3 :The third quartile (Q3) is the middle value between the median and the highest value of the data set.

Step 4 :By calculating, we find that the first quartile (Q1) is 12 and the third quartile (Q3) is 24.

Step 5 :Final Answer: The first quartile of these data is \(\boxed{12}\). The third quartile of these data is \(\boxed{24}\).

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