Here are the science test scores from Ms. O'Donnell's class
55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100 Find the MAD.
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1155 / 17
Mean = 67.94
Absolute deviations:
|55 - 67.94| = 12.94
|60 - 67.94| = 7.94
|70 - 67.94| = 2.06
|70 - 67.94| = 2.06
|75 - 67.94| = 7.06
|75 - 67.94| = 7.06
|75 - 67.94| = 7.06
|80 - 67.94| = 12.06
|80 - 67.94| = 12.06
|85 - 67.94| = 17.06
|85 - 67.94| = 17.06
|85 - 67.94| = 17.06
|85 - 67.94| = 17.06
|90 - 67.94| = 22.06
|90 - 67.94| = 22.06
|95 - 67.94| = 27.06
|100 - 67.94| = 32.06
MAD = (12.94 + 7.94 + 2.06 + 2.06 + 7.06 + 7.06 + 7.06 + 12.06 + 12.06 + 17.06 + 17.06 + 17.06 + 17.06 + 22.06 + 22.06 + 27.06 + 32.06) / 17
MAD ≈ 13.18
Therefore, the Mean Absolute Deviation (MAD) is approximately 13.18.
Wrong
To find the Mean Absolute Deviation (MAD), follow these steps:
1. Calculate the mean of the test scores:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1290 / 17
Mean = 76.47
2. Find the absolute deviations from the mean for each score:
|55 - 76.47| = 21.47
|60 - 76.47| = 16.47
|70 - 76.47| = 6.47
|70 - 76.47| = 6.47
|75 - 76.47| = 1.47
|75 - 76.47| = 1.47
|75 - 76.47| = 1.47
|80 - 76.47| = 3.53
|80 - 76.47| = 3.53
|85 - 76.47| = 8.53
|85 - 76.47| = 8.53
|85 - 76.47| = 8.53
|85 - 76.47| = 8.53
|90 - 76.47| = 13.53
|90 - 76.47| = 13.53
|95 - 76.47| = 18.53
|100 - 76.47| = 23.53
3. Calculate the sum of the absolute deviations:
Sum of absolute deviations = 21.47 + 16.47 + 6.47 + 6.47 + 1.47 + 1.47 + 1.47 + 3.53 + 3.53 + 8.53 + 8.53 + 8.53 + 8.53 + 13.53 + 13.53 + 18.53 + 23.53 = 150.97
4. Find the MAD by dividing the sum of absolute deviations by the number of scores:
MAD = 150.97 / 17
MAD ≈ 8.88
Therefore, the Mean Absolute Deviation (MAD) for the given test scores is approximately 8.88.
Wrong again
Apologies for the errors in the previous calculations. Let's correct that:
1. Calculate the mean of the test scores:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1265 / 17
Mean ≈ 74.41
2. Find the absolute deviations from the mean for each score:
|55 - 74.41| = 19.41
|60 - 74.41| = 14.41
|70 - 74.41| = 4.41
|70 - 74.41| = 4.41
|75 - 74.41| = 0.59
|75 - 74.41| = 0.59
|75 - 74.41| = 0.59
|80 - 74.41| = 5.59
|80 - 74.41| = 5.59
|85 - 74.41| = 10.59
|85 - 74.41| = 10.59
|85 - 74.41| = 10.59
|85 - 74.41| = 10.59
|90 - 74.41| = 15.59
|90 - 74.41| = 15.59
|95 - 74.41| = 20.59
|100 - 74.41| = 25.59
3. Calculate the sum of the absolute deviations:
Sum of absolute deviations = 19.41 + 14.41 + 4.41 + 4.41 + 0.59 + 0.59 + 0.59 + 5.59 + 5.59 + 10.59 + 10.59 + 10.59 + 10.59 + 15.59 + 15.59 + 20.59 + 25.59
Sum of absolute deviations = 162.21
4. Find the MAD by dividing the sum of absolute deviations by the number of scores (17):
MAD = 162.21 / 17
MAD ≈ 9.54
Therefore, the corrected Mean Absolute Deviation (MAD) for the given test scores is approximately 9.54. Thank you for your patience.