#### Definition

- The mean absolute error (mae) is a metric for determining the similarity between two sets.
- The error between two numbers is simply the difference between them.
- The absolute error is the absolute difference.
- To find the mean absolute error:
- Find the absolute error between corresponding values in the sets
- Then find the mean of those errors.

#### Example

- Find the mean absolute error of the following two sets of numbers:
`S`_{1} = [2, 5, 9, 2]
S_{2} = [6, 3, 6, 1]

- First we calculate the differences between these numbers:
```
D = [2 - 6, 5 - 3, 9 - 6, 2 - 1]
D = [-4, 2, 3, 1]
```

- Now we must make these numbers absolute:
`D = [4, 2, 3, 1]`

- Finally, we find the mean of these numbers:
```
mae = (4 + 2 + 3 + 1) / 4
mae = 10 / 4
mae = 2.5
```

#### Mathematical Definition

LaTeX formula:`mae = (\frac{1}{n})\sum_{i=1}^{n}\left | y_{i} - x_{i} \right |`

#### Code (Python)

```
import sklearn.metrics
S1 = [2, 5, 9, 2]
S2 = [6, 3, 6, 1]
mae = sklearn.metrics.mean_absolute_error(S1, S2)
print(mae)
```