Question

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
.

Answer 1

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:
\[
\boxed{1.75}
\]