To calculate the average deviation from the mean for each dataset, we first need to find the deviations of each value from the mean, take the absolute values of these deviations, sum them up, and then divide by the number of observations in each dataset.
Dataset A: {7, 9, 9, 12}
Mean = 9.25
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Calculate deviations from the mean:
- |7 - 9.25| = | -2.25| = 2.25
- |9 - 9.25| = | -0.25| = 0.25
- |9 - 9.25| = | -0.25| = 0.25
- |12 - 9.25| = | 2.75| = 2.75
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Sum of absolute deviations: \[ 2.25 + 0.25 + 0.25 + 2.75 = 5.5 \]
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Average deviation: \[ \text{Average Deviation} = \frac{5.5}{4} = 1.375 \]
Dataset B: {6, 8, 10, 13}
Mean = 9.25
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Calculate deviations from the mean:
- |6 - 9.25| = | -3.25| = 3.25
- |8 - 9.25| = | -1.25| = 1.25
- |10 - 9.25| = | 0.75| = 0.75
- |13 - 9.25| = | 3.75| = 3.75
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Sum of absolute deviations: \[ 3.25 + 1.25 + 0.75 + 3.75 = 9.0 \]
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Average deviation: \[ \text{Average Deviation} = \frac{9.0}{4} = 2.25 \]
Summary of Results
- The average deviation from the mean of dataset A is 1.375.
- The average deviation from the mean of dataset B is 2.25.