Answer
$Q_1=6.12$
$Q_2=8.46$
$Q_3=10.06$
$Q_1=6.12$ means that 25% of the carbon dioxide emissions are less than or equal to 6.12 and 75% of the carbon dioxide emissions are greater than 6.12
$Q_2=8.46$ means that 50% of the carbon dioxide emissions are less than or equal to 8.46 and 50% of the carbon dioxide emissions are greater than 8.46
$Q_3=10.06$ means that 75% of the carbon dioxide emissions are less than or equal to 10.06 and 25% of the carbon dioxide emissions are greater than 10.06
Work Step by Step
In ascending order: 1.31, 3.57, 3.58, 4.09, 4.63, 5.38, 5.40, 5.73, 6.12, 6.24, 6.48, 6.93, 7.31, 7.76, 7.82, 7.94, 8.33, 8.59, 8.70, 8.86, 9.38, 9.46, 9.91, 9.94, 9.95, 10.06, 10.36, 10.71, 11.06, 14.87, 15.86, 16.75, 23.87, 161.57
The second quartile is equal to the median. Since we have 34 observations, the median is the mean between the 17th and the 18th observations in ascending order:
$Q_2=\frac{8.33+8.59}{2}=8.46$
The botton half of the data: 1.31, 3.57, 3.58, 4.09, 4.63, 5.38, 5.40, 5.73, 6.12, 6.24, 6.48, 6.93, 7.31, 7.76, 7.82, 7.94, 8.33. $Q_1$ is the median of these values. Since there are 17 observations, the median is the 9th observation in ascending order:
$Q_1=6.12$
The top half of the data: 8.59, 8.70, 8.86, 9.38, 9.46, 9.91, 9.94, 9.95, 10.06, 10.36, 10.71, 11.06, 14.87, 15.86, 16.75, 23.87, 161.57. $Q_3$ is the median of these values. Since there are 17 observations, the median is the 9th observation in ascending order:
$Q_3=10.06$
