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 32 38 40 48 49 49 52 86 97 send data to excel part: 0 / 4 part 1 of 4 find the first and third quartiles of these data. the first quartile is. the third quartile is.

Explanation:

Step1: Determine the number of data points

The data set has $n = 30$ values.

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

The position of $Q_1$ is $L_{Q_1}=\frac{1}{4}(n + 1)=\frac{1}{4}(30+ 1)=7.75$.
The first - quartile is the value at the 7.75th position. We take the 7th value ($12$) and the 8th value ($12$). Using the formula for interpolation $Q_1=12+(0.75)(12 - 12)=12$.

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

The position of $Q_3$ is $L_{Q_3}=\frac{3}{4}(n + 1)=\frac{3}{4}(30 + 1)=23.25$.
The third - quartile is the value at the 23.25th position. We take the 23rd value ($40$) and the 24th value ($48$). Using the formula for interpolation $Q_3=40+(0.25)(48 - 40)=42$.

Answer:

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