The mean absolute deviation is: B. 1.3 pounds; the weight of 1 bag varies 1.3 pounds from the mean on average.
First, find the mean of the data then find the average of the distance of every data point from the mean.
Given the data:
6, 4, 8, 7, 8, 9
Find the Mean:
Mean = (6 + 4 + 8 + 7 + 8 + 9) / 6
Mean = 7
Find the Absolute Value of Difference Between Each Number and the Mean:
Difference = |xi - mean|
Difference x1 = |6 - 7| = 1
Difference x2 = |4 - 7| = 3
Difference x3 = |8 - 7| = 1
Difference x4 = |7 - 7| = 0
Difference x5 = |8 - 7| = 1
Difference x6 = |9 - 7| = 2
Find the Mean Absolute Deviation:
Mean absolute deviation = Sum of Differences / n Sum of Differences = (1 + 3 + 1 + 0 + 1 + 2)
Sum of differences = 8
Mean absolute deviation = 8 / 6 ≈ 1.3 pounds
Therefore, this means that, the mean absolute deviation is: B. 1.3 pounds; the weight of 1 bag varies 1.3 pounds from the mean on average.
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