Mrs. Feinstein recorded the weight, in pounds, of each of her 8 great-grandchildren. Her data are shown.
45, 52, 31, 27, 38, 60, 44, 55
What is the mean absolute deviation of the data?
A.
0 pounds
B.
9 pounds
C.
10 pounds
D.
44 pounds
To find the mean absolute deviation, first find the mean (average) of the data:
(45 + 52 + 31 + 27 + 38 + 60 + 44 + 55) / 8 = 42.5
Next, find the absolute deviation of each data point from the mean by subtracting the mean from each data point and taking the absolute value:
|45 - 42.5| = 2.5
|52 - 42.5| = 9.5
|31 - 42.5| = 11.5
|27 - 42.5| = 15.5
|38 - 42.5| = 4.5
|60 - 42.5| = 17.5
|44 - 42.5| = 1.5
|55 - 42.5| = 12.5
Then, find the average of these absolute deviations:
(2.5 + 9.5 + 11.5 + 15.5 + 4.5 + 17.5 + 1.5 + 12.5) / 8 ≈ 9
Therefore, the mean absolute deviation of the data is approximately 9 pounds, which is answer choice B.