To calculate the mean absolute deviation (MAD) of the weights of the puppies, follow these steps:
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Calculate the mean of the weights. We have the weights: \( 3, 1.6, 2.8, 2.5, 1.7, 2.8 \).
First, sum the weights: \[ 3 + 1.6 + 2.8 + 2.5 + 1.7 + 2.8 = 14.4 \]
Next, divide by the number of puppies (6) to find the mean: \[ \text{Mean} = \frac{14.4}{6} = 2.4 \]
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Calculate the absolute deviations from the mean. Calculate the absolute difference between each weight and the mean:
- For \(3\): \[ |3 - 2.4| = 0.6 \]
- For \(1.6\): \[ |1.6 - 2.4| = 0.8 \]
- For \(2.8\): \[ |2.8 - 2.4| = 0.4 \]
- For \(2.5\): \[ |2.5 - 2.4| = 0.1 \]
- For \(1.7\): \[ |1.7 - 2.4| = 0.7 \]
- For \(2.8\) (again): \[ |2.8 - 2.4| = 0.4 \]
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Sum the absolute deviations. Now add up all the absolute deviations: \[ 0.6 + 0.8 + 0.4 + 0.1 + 0.7 + 0.4 = 3.0 \]
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Calculate the mean absolute deviation. Divide the sum of the absolute deviations by the number of puppies (6): \[ \text{Mean Absolute Deviation} = \frac{3.0}{6} = 0.5 \]
Therefore, the mean absolute deviation of the weights of the puppies is \( \boxed{0.5} \).