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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) Responses Dataset #1 and Dataset #2 are equally spread because they both have a mean absolute deviation of 0. Dataset #1 and Dataset #2 are equally spread because they both have a mean absolute deviation of 0. 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 #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 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 #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 #1 and Dataset #2 are equally spread because they both have a mean of 62

1 answer

To determine which dataset is less spread out, we can calculate the mean absolute deviation (MAD) for each dataset. The mean absolute deviation is calculated as follows:

  1. Find the mean of the dataset (which we know is 62 for both datasets).
  2. Calculate the absolute deviation of each value from the mean.
  3. Find the average of these absolute deviations.

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

  • Mean = 62

  • Absolute deviations:

    • |51 - 62| = 11
    • |53 - 62| = 9
    • |56 - 62| = 6
    • |60 - 62| = 2
    • |72 - 62| = 10
    • |80 - 62| = 18

  • Sum of absolute deviations = 11 + 9 + 6 + 2 + 10 + 18 = 56

  • Mean absolute deviation (MAD) for Dataset #1 = 56 / 6 ≈ 9.3

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

  • Mean = 62

  • Absolute deviations:

    • |49 - 62| = 13
    • |55 - 62| = 7
    • |61 - 62| = 1
    • |63 - 62| = 1
    • |70 - 62| = 8
    • |74 - 62| = 12

  • Sum of absolute deviations = 13 + 7 + 1 + 1 + 8 + 12 = 42

  • Mean absolute deviation (MAD) for Dataset #2 = 42 / 6 ≈ 7.0

Conclusion:

  • MAD for Dataset #1 = 9.3
  • MAD for Dataset #2 = 7.0

Since the mean absolute deviation of Dataset #2 (7.0) is less than that of Dataset #1 (9.3), Dataset #2 is less spread out.

The correct response is:

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.