To determine which summary statistics should be used to compare the two data sets of student heights, we need to consider the shape of the distributions.
If the data sets are skewed (that is, they are not symmetrically distributed, potentially having a long tail on one side), the best summary statistics to use are the median and the interquartile range (IQR). This is because the median is a measure of central tendency that is not affected by extreme values (outliers) and the IQR provides a measure of variability that indicates the range within which the middle 50% of the data lies.
Conversely, the mean and standard deviation are more appropriate for symmetric distributions because they assume a normal-like distribution where the data is evenly distributed around the mean.
Considering this information, the correct option is:
The median and the interquartile range because the data sets are skewed.