Problem

Class A reading times are \(12,~15,~18,~18,~21,~24,~27,~\text{and}~30~\text{minutes}\). Class B has mean \(21~\text{minutes}\), median \(19.5~\text{minutes}\), range \(18~\text{minutes}\), and interquartile range \(12~\text{minutes}\). For Class A's quartiles, split the ordered data into \(\text{two}~\text{groups}~\text{of}~\text{four}\) and take each half's median. Which comparison of Class A and Class B is correct?

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What this problem is really about

Put Class A into the same four-statistic format already given for Class B. From the ordered data, compute total-over-count, average the two middle values, subtract endpoints, and split into two groups of four for the quartiles. Then compare center with center and spread with the same spread measure, preserving minutes throughout.

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Class A: mean 21 min, median 19.5 min, range 18 min, IQR 9 min. Class B: mean 21 min, median 19.5 min, range 18 min, IQR 12 min. Same median: yes. Same range: yes.

Class A: mean 20.625 min, median 19.5 min, range 30 min, IQR 9 min. Class B: mean 21 min, median 19.5 min, range 18 min, IQR 12 min. Same median: yes. Same range: no.

Class A: mean 20.625 min, median 19.5 min, range 18 min, IQR 12 min. Class B: mean 21 min, median 19.5 min, range 18 min, IQR 12 min. Same median: yes. Same range: yes.

Class A: mean 20.625 min, median 19.5 min, range 18 min, IQR 9 min. Class B: mean 21 min, median 19.5 min, range 18 min, IQR 12 min. Same median: yes. Same range: yes.

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