Problem

Group 1 has mean \(14\), median \(13\), range \(10\), and interquartile range \(6\). Group 2 scores are \(8\), \(10\), \(11\), \(13\), \(13\), \(15\), \(17\), and \(18\). For Group 2's quartiles, split the ordered data into \(\text{two}~\text{groups}~\text{of}~\text{four}\) and take each half's median. Which comparison of Group 1 and Group 2 is correct?

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Group 1: mean 14, median 13, range 10, IQR 6; Group 2: mean 13.125, median 13, range 10, IQR 4. Group 1 has the higher center, and Group 2 has the smaller spread.

Group 1: mean 14, median 13, range 10, IQR 6; Group 2: mean 13.125, median 13, range 10, IQR 5.5. Group 1 has the higher center by mean, and Group 1 has the greater spread by IQR.

Group 2: mean 13, median 13, range 10, IQR 5.5. The groups have the same center because both medians are 13, and the same spread because both ranges are 10.

Group 1: mean 14, median 13, range 10, IQR 6; Group 2: mean 13.5, median 13, range 10, IQR 5.5. Group 1 has the higher center by mean, and Group 1 has the greater spread by IQR.

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