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Find the mean absolute deviation of the following dataset. Express your answer as a decimal.

{21,25,25,26,26,27,28,30}
(1 point)
The mean absolute deviation is
.

1 answer

To find the mean absolute deviation (MAD) of the dataset {21, 25, 25, 26, 26, 27, 28, 30}, follow these steps:

  1. Calculate the mean of the dataset. \[ \text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} = \frac{21 + 25 + 25 + 26 + 26 + 27 + 28 + 30}{8} \] \[ = \frac{208}{8} = 26 \]

  2. Calculate the absolute deviations from the mean. \[ |21 - 26| = 5 \] \[ |25 - 26| = 1 \] \[ |25 - 26| = 1 \] \[ |26 - 26| = 0 \] \[ |26 - 26| = 0 \] \[ |27 - 26| = 1 \] \[ |28 - 26| = 2 \] \[ |30 - 26| = 4 \]

    The absolute deviations are {5, 1, 1, 0, 0, 1, 2, 4}.

  3. Calculate the mean of the absolute deviations. \[ \text{Mean Absolute Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of data points}} = \frac{5 + 1 + 1 + 0 + 0 + 1 + 2 + 4}{8} \] \[ = \frac{14}{8} = 1.75 \]

Thus, the mean absolute deviation of the dataset is: \[ \boxed{1.75} \]