Answer
115 and 1000 are outliers.
Work Step by Step
In ascending order: 7, 8, 9, 10, 12, 13, 14, 16, 20, 21, 21, 22, 22, 26, 26, 27, 28, 28, 32, 33, 33, 35, 36, 36, 38, 39, 48, 50, 51, 54, 54, 59, 64, 65, 67, 75, 80, 101, 115, 1000
There are 40 observations. $Q_2=median$ is the mean between the 20th and the 21th observations in ascending order:
$Q_2=\frac{33+33}{2}=33$
The botton half of the data: 7, 8, 9, 10, 12, 13, 14, 16, 20, 21, 21, 22, 22, 26, 26, 27, 28, 28, 32, 33. $Q_1$ is the median of these values. Since there are 20 observations, the median is the mean between the 10th and the 11th observation in ascending order:
$Q_1=\frac{21+21}{2}=21$
The top half of the data: 33, 35, 36, 36, 38, 39, 48, 50, 51, 54, 54, 59, 64, 65, 67, 75, 80, 101, 115, 1000. $Q_3$ is the median of these values. Since there are 20 observations, the median is the mean between the 10th and the 11th observation in ascending order:
$Q_3=\frac{54+54}{2}=54$
$IQR=Q_3-Q_1=54-21=33$
$Lower~fence=Q_1-1.5\times IQR=-28.5$
$Upper~fence=Q_3+1.5\times IQR=103.5$
Since 115 and 1000 are greater than 103.5, they are outliers. There are no other outliers.
