Question

The mean of each dataset that follows is 62. Which dataset is less spread out? Justify your answer using the mean absolute deviation of each dataset. Round your answers to the nearest tenth.

Dataset #1: {51,53,56,60,72,80}

Dataset #2: {49,55,61,63,70,74}


(1 point)

Dataset #1 and Dataset #2 are equally spread because they both have a mean of 62.

Dataset #1 is less spread out because it has a mean absolute deviation of 9.3 whereas Dataset #2 has a mean absolute deviation of 7.

Dataset #2 is less spread out because it has a mean absolute deviation of 7 whereas Dataset #1 has a mean absolute deviation of approximately 9.3.

Dataset #1 and Dataset #2 are equally spread because they both have a mean absolute deviation of 0.
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Answer 1

Dataset #1 deviations: 11, 9, 6, 2, 10, 18 → MAD = (11+9+6+2+10+18)/6 = 56/6 ≈ 9.3

Dataset #2 deviations: 13, 7, 1, 1, 8, 12 → MAD = (13+7+1+1+8+12)/6 = 42/6 = 7.0

Dataset #2 is less spread out because its mean absolute deviation (7.0) is smaller than Dataset #1's (9.3).