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 1 of 4
find the first and third quartiles of these data.
the first quartile is 12.
the third quartile is 38.
part 2 of 4
find the median of these data.
median = 19
part 3 of 4
find the lower and upper outlier boundaries.
lower outlier boundary is - 27.
upper outlier boundary is 77.
part 4 of 4
are there any outliers? if so, list them. otherwise, select
one.\

Explanation:

Step1: Count data points

There are 30 data - points.

Step2: Find the median position

The median position for \(n = 30\) data - points is \(\frac{n+1}{2}=\frac{30 + 1}{2}=15.5\). The median is the average of the 15th and 16th ordered data - points. The 15th value is 19 and the 16th value is 19, so the median \(M = 19\).

Step3: Find the first - quartile position

The position of the first quartile \(Q_1\) is \(\frac{n + 1}{4}=\frac{30+1}{4}=7.75\). The first quartile is the value at the 8th position, so \(Q_1 = 12\).

Step4: Find the third - quartile position

The position of the third quartile \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(30 + 1)}{4}=23.25\). The third quartile is the value at the 24th position, so \(Q_3=38\).

Step5: Calculate the inter - quartile range (IQR)

\(IQR=Q_3 - Q_1=38 - 12 = 26\).

Step6: Calculate the lower outlier boundary

Lower outlier boundary \(=Q_1-1.5\times IQR=12-1.5\times26=12 - 39=-27\).

Step7: Calculate the upper outlier boundary

Upper outlier boundary \(=Q_3 + 1.5\times IQR=38+1.5\times26=38 + 39 = 77\).

Answer:

Median: 19
First quartile (\(Q_1\)): 12
Third quartile (\(Q_3\)): 38
Lower outlier boundary: - 27
Upper outlier boundary: 77