To calculate the average deviation from the mean for each dataset, follow these steps:
- Calculate the deviations from the mean for each data point in the dataset.
- Take the absolute value of each deviation.
- Calculate the mean of these absolute deviations (this is the average deviation from the mean).
Dataset A: {7, 9, 9, 12}
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Mean = 9.25
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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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Absolute deviations: {2.25, 0.25, 0.25, 2.75}
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Average deviation for Dataset A: \[ \text{Average Deviation} = \frac{2.25 + 0.25 + 0.25 + 2.75}{4} = \frac{5.5}{4} = 1.375 \]
Dataset B: {6, 8, 10, 13}
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Mean = 9.25
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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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Absolute deviations: {3.25, 1.25, 0.75, 3.75}
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Average deviation for Dataset B: \[ \text{Average Deviation} = \frac{3.25 + 1.25 + 0.75 + 3.75}{4} = \frac{9.0}{4} = 2.25 \]
Final 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.
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