Calculate the Mean Absolute Error (MAE) between predicted and observed values. Input your values and visualize the differences between them.

**Mean Absolute Error (MAE):**

## Understanding Mean Absolute Error (MAE)

The **Mean Absolute Error (MAE)** is a metric used to evaluate the accuracy of a model in predicting quantitative data. It calculates the average of the absolute differences between the predicted values and the actual observed values. The lower the MAE, the closer the predicted values are to the actual values.

### Why Use MAE?

MAE provides an intuitive measure of error because it uses the absolute difference between the predicted and observed values, ignoring the direction of the error (i.e., whether the prediction was higher or lower than the observed value). This makes it a simple and easy-to-understand error metric. Since the errors are not squared, large errors do not get overly penalized (unlike in MSE).

### Formula for Mean Absolute Error

Where:

- \(n\) is the number of data points
- \(P_{i}\) is the predicted value for the \(i^{th}\) data point
- \(O_{i}\) is the observed (actual) value for the \(i^{th}\) data point

### Example Calculation

Suppose we have the following predicted and observed values:

- Predicted values: [2.3, 3.1, 4.0]
- Observed values: [2.5, 3.0, 3.8]

Let’s calculate the MAE using the formula:

**Step 1:** Compute the absolute differences between each pair of predicted and observed values:

- Difference 1: \( |2.3 - 2.5| = 0.2 \)
- Difference 2: \( |3.1 - 3.0| = 0.1 \)
- Difference 3: \( |4.0 - 3.8| = 0.2 \)

**Step 2:** Sum the absolute differences:

- \( 0.2 + 0.1 + 0.2 = 0.5 \)

**Step 3:** Divide by the number of data points (\(n = 3\)):

- \( \text{MAE} = \frac{0.5}{3} \approx 0.167 \)

Therefore, the Mean Absolute Error (MAE) for this example is approximately **0.167**.

### MAE vs. Other Error Metrics

While MAE is an effective metric for measuring error, there are other common metrics used for evaluating model performance, such as Mean Squared Error (MSE) and Root Mean Squared Error (RMSE). MAE treats all errors equally, while MSE and RMSE give higher weight to larger errors because they square the differences. This makes MAE less sensitive to outliers than MSE or RMSE.

### Applications of MAE

MAE is widely used in fields such as:

**Weather forecasting**: To evaluate the accuracy of temperature, precipitation, or other weather predictions.**Financial modeling**: To measure how well financial models predict future stock prices, interest rates, or other variables.**Machine learning**: Used in regression tasks to evaluate the performance of models predicting continuous values.

### Further Reading

## Implementations

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.