Question: Recall that the interquartile range covers the middle 50% of the data. For a bell-shaped population:
a. The interquartile range covers what range of standardized scores? In other words, what are the standardized scores for the lower and upper quartiles?
b. How many standard deviations are covered by the interquartile range?
c. The whiskers on a boxplot can extend a total of 2 interquartile ranges on either side of the median, which for a bell-shaped population is equal to the mean. (They can extend 1.5 IQR outside of the box but the distance between the median/mean and end of the box is an additional 0.5 IQR.) Beyond that range, data values are considered to be outliers. In other words, for bell shaped populations, data values are outliers if they are more than 2 IQRs away from the mean. At what percentiles (at the upper and lower ends) are data values considered to be outliers for bell-shaped populations?