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

1. **Calculate the Mean**:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{21 + 25 + 25 + 26 + 26 + 27 + 28 + 30}{8}
\]
\[
= \frac{ 21 + 25 + 25 + 26 + 26 + 27 + 28 + 30 }{8} = \frac{ 8 \times 25 + 4 + 2 }{8} = \frac{200 + 6}{8} = \frac{206}{8} = 25.75
\]

2. **Calculate the Absolute Deviations from the Mean**:
\[
|21 - 25.75| = | -4.75| = 4.75
\]
\[
|25 - 25.75| = | -0.75| = 0.75
\]
\[
|25 - 25.75| = | -0.75| = 0.75
\]
\[
|26 - 25.75| = | 0.25| = 0.25
\]
\[
|26 - 25.75| = | 0.25| = 0.25
\]
\[
|27 - 25.75| = | 1.25| = 1.25
\]
\[
|28 - 25.75| = | 2.25| = 2.25
\]
\[
|30 - 25.75| = | 4.25| = 4.25
\]

3. **Sum the Absolute Deviations**:
\[
4.75 + 0.75 + 0.75 + 0.25 + 0.25 + 1.25 + 2.25 + 4.25 = 10.5
\]

4. **Calculate the Mean Absolute Deviation**:
\[
\text{MAD} = \frac{\text{Sum of absolute deviations}}{\text{Number of values}} = \frac{10.5}{8} = 1.3125
\]

Thus, the mean absolute deviation is \( \boxed{1.3125} \).