To calculate the average deviation from the mean for the dataset {1, 1, 3, 5, 8}, we will follow these steps:
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Calculate the mean: \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \] The sum of the values is: \[ 1 + 1 + 3 + 5 + 8 = 18 \] The number of values is 5. Thus, the mean is: \[ \text{Mean} = \frac{18}{5} = 3.6 \]
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Calculate the absolute deviations from the mean: \[ |x_i - \text{mean}| \]
- For 1: \( |1 - 3.6| = 2.6 \)
- For 1: \( |1 - 3.6| = 2.6 \)
- For 3: \( |3 - 3.6| = 0.6 \)
- For 5: \( |5 - 3.6| = 1.4 \)
- For 8: \( |8 - 3.6| = 4.4 \)
The absolute deviations are: {2.6, 2.6, 0.6, 1.4, 4.4}
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Calculate the average of these absolute deviations: \[ \text{Average Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of values}} \] The sum of the absolute deviations is: \[ 2.6 + 2.6 + 0.6 + 1.4 + 4.4 = 11.6 \] Thus, the average deviation is: \[ \text{Average Deviation} = \frac{11.6}{5} = 2.32 \]
Finally, the average deviation from the mean is 2.32.