Final answer:
The IQR for the males' data is estimated at 12 by subtracting the first quartile from the third quartile. The median should be used as a better measure of center in skewed distributions. Outliers can be errors or significant deviations needing investigation.
Step-by-step explanation:
Part A: To estimate the IQR for the males' data, we use the provided third quartile (Q3) and first quartile (Q1). The IQR is calculated as Q3 - Q1 which is 92 - 80, resulting in an IQR of 12.
Part B: To estimate the difference between the median values of each data set, we would need to know the median for the other data set. The median for males is not explicitly provided, but assuming it is the same as the median represented by the vertical line in the box at 86, we would subtract the median of the other group from 86 to find the difference.
Part C: Describing the distribution of the data and deciding whether the mean or median would be a better measure of center depends on the shape of the distribution. If the distribution is symmetric, the mean would be an appropriate measure. However, if the distribution is skewed, the median is generally a better representation of the center as it is not affected by outliers or non-symmetrical data sets, as noted in item 48 where the median is preferred due to distortion from a high value house.
Part D: A possible reason for an outlier in the data set could be an error in data collection, entry, or a genuine extreme value which is significantly different from other data points. Outliers can sometimes indicate special cases or errors and should be investigated further.