Question

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. 2 3 5 9 9 11 12 12 13 13 14 15 15 16 19 19 20 21 25 26 32 35 38 40 48 49 49 52 86 97. find the first and third quartiles of these data. the first quartile is . the third quartile is .

Explanation:

Step1: Count the number of data points

There are $n = 30$ data - points.

Step2: Calculate the position of the first quartile ($Q_1$)

The position of $Q_1$ is $L_{Q_1}=\frac{n + 1}{4}=\frac{30+1}{4}=7.75$. Since it is not an integer, we interpolate. The 7th value is 12 and the 8th value is 12. $Q_1=12+(0.75)\times(12 - 12)=12$.

Step3: Calculate the position of the third quartile ($Q_3$)

The position of $Q_3$ is $L_{Q_3}=\frac{3(n + 1)}{4}=\frac{3\times(30 + 1)}{4}=23.25$. The 23rd value is 40 and the 24th value is 48. $Q_3=40+(0.25)\times(48 - 40)=42$.

Answer:

The first quartile is 12.
The third quartile is 42.