Question:

Carlton found data on the percent of area that is covered by water for each of the 50 states in the U.S. He made the dotplots below to compare the distributions for states that border an ocean and states that do not border an ocean.

Which of the following is the best statistical reason for using the median and interquartile range (IQR), rather than the mean and standard deviation, to compare the centers and spreads of these distributions?

(A) The mean and standard deviation are more strongly influenced by outliers than the median and IQR.

(B) The median and IQR are easier to calculate than the mean and standard deviation.

(C) The two groups contain different numbers of states, so the standard deviation is not appropriate.

(D) The two distributions have the same shape.

Level:

### Standards

S-ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).
S-ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more di"erent data sets.
S-ID.3: Interpret di"erences in shape, center, and spread in the context of the data sets, accounting for possible e"ects of extreme data points (outliers).