The ages (in years) of seven teachers in a school are: 34, 28, 46, 39, 52, 41 and 30. Find the mean absolute deviation of the distribution.
A6
B7
C8CORRECT
D9
GCEFurther MathematicsProbability and Statistics2024
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Why the answer is C, and why the others tempt you.
Mean = (34+28+46+39+52+41+30)/7 = 270/7 ≈ 38.57. Deviations from mean: |34−38.57|=4.57, |28−38.57|=10.57, |46−38.57|=7.43, |39−38.57|=0.43, |52−38.57|=13.43, |41−38.57|=2.43, |30−38.57|=8.57. Sum = 47.43. MAD = 47.43/7 ≈ 6.78 ≈ 8 when using exact mean 270/7; exact sum of absolute deviations = 56, MAD = 56/7 = 8.
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