Following are summary statistics for two data sets, A and B.
a. Compute the interquartile ranges for both A and B.
b. Do the summary statistics for A provide enough information to construct a boxplot? If so, construct the boxplot. If not, explain why.
c. Do the summary statistics for B provide enough information to construct a boxplot? If so, construct the boxplot. If not, explain why.
(a) IQR = 3rd quartile – 1st quartile. A: IQR = 6.02 – 1.42 = 4.60, B: IQR = 9.13 – 5.27 = 3.86
(b) Yes, since the minimum is within 1.5 IQR of the first quartile and the maximum is within 1.5 IQR of the third quartile, there are no outliers, and the given numbers specify the boundaries of the box and the ends of the whiskers.
(c) No. The minimum value of –2.235 is an “outlier,” since it is more than 1.5 times the interquartile range below the first quartile. The lower whisker should extend to the smallest point that is not an outlier, but the value of this point is not given.
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