The authors of the paper "Delayed Time to Defibrillation after In-Hospital Cardiac Arrest" (New England Journal of Medicine [2008]: 9-16) described a study of how survival is related to the length of time it takes from the time of a heart attack to the administration of defibrillation therapy. The following is a statement from the paper:
We identified 6789 patients from 369 hospitals who had in-hospital cardiac arrest due to ventricular fibrillation (69.7%) or pulseless ventricular trachycardia (30.3%). Overall, the median time to de- fibrillation was 1 minute (interquartile range [was] 3 minutes).
Data from the paper on time to defibrillation (in minutes) for these 6789 patients was used to produce the following Minitab output and boxplot.
a. Why is there no lower whisker in the given boxplot?
b. How is it possible for the median, the lower quartile, and the minimum value in the data set to all be equal? (Note-this is why you do not see a median line in the box part of the boxplot.)
c. The authors of the paper considered a time to defibrillation of greater than 2 minutes as unacceptable. Based on the given boxplot and summary statistics, is it possible that the percentage of patients having an unacceptable time to defibrillation is greater than 50%? Greater than 25%? Less than 25%? Explain.
Descriptive Statistics: Time to Defibrillation
Variable N Mean StDev Minimum Q1 Median Q3 Maximum Time 6789 2.3737 2.0713 1.0000 1.0000 1.0000 3.0000 7.0000
d. Is the outlier shown at 7 a mild outlier or an extreme outlier?