To calculate the mean absolute deviation (MAD) of the dataset, we follow these steps:
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Calculate the Mean: First, we find the mean (average) of the dataset.
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]
The sum of the values is: \[ 125 + 198 + 209 + 213 + 101 + 178 = 1024 \]
The number of values is 6.
Thus, the mean is: \[ \text{Mean} = \frac{1024}{6} \approx 170.67 \]
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Calculate the Absolute Deviations: Now we calculate the absolute deviations of each value from the mean:
\[ |125 - 170.67| = | -45.67 | \approx 45.67 \] \[ |198 - 170.67| = |27.33| \approx 27.33 \] \[ |209 - 170.67| = |38.33| \approx 38.33 \] \[ |213 - 170.67| = |42.33| \approx 42.33 \] \[ |101 - 170.67| = | -69.67 | \approx 69.67 \] \[ |178 - 170.67| = |7.33| \approx 7.33 \]
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Calculate the Mean Absolute Deviation (MAD): We sum these absolute deviations and then divide by the number of values.
The sum of the absolute deviations is: \[ 45.67 + 27.33 + 38.33 + 42.33 + 69.67 + 7.33 = 230.67 \]
Now, we calculate the MAD: \[ \text{MAD} = \frac{230.67}{6} \approx 38.445 \]
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Round to the Nearest Tenth: Rounding \(38.445\) to the nearest tenth gives us \(38.4\).
Therefore, the mean absolute deviation of the dataset is approximately 38.4.