To calculate the average error, you sum the absolute values of all individual errors and then divide that sum by the total number of errors.
Here's a more detailed breakdown:
Understanding Average Error
Average error is a measure of the overall difference between predicted or measured values and the actual or true values. It provides a general sense of how well a model or measurement performs on average, without considering the direction of the errors (whether they are over- or under-estimations).
Steps to Calculate Average Error:
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Determine the individual errors: For each data point, subtract the actual value from the predicted or measured value. This gives you the error for each point.
Error = Predicted Value - Actual Value -
Calculate the absolute value of each error: Take the absolute value of each error. This ensures that all errors are treated as positive values, regardless of whether they are positive or negative. This is important because positive and negative errors can cancel each other out if you simply sum them directly.
Absolute Error = |Error| = |Predicted Value - Actual Value| -
Sum the absolute errors: Add up all the absolute errors calculated in the previous step.
Sum of Absolute Errors = |Error1| + |Error2| + |Error3| + ... + |ErrorN| -
Divide by the number of errors: Divide the sum of the absolute errors by the total number of data points (N). This gives you the average error.
Average Error = (Sum of Absolute Errors) / N
Example:
Let's say you are predicting the price of a stock each day for a week. Here's a table showing the predicted price, actual price, and the calculation of the average error:
| Day | Predicted Price | Actual Price | Error (Predicted - Actual) | Absolute Error |
|---|---|---|---|---|
| 1 | $52 | $50 | $2 | $2 |
| 2 | $51 | $53 | -$2 | $2 |
| 3 | $54 | $55 | -$1 | $1 |
| 4 | $53 | $52 | $1 | $1 |
| 5 | $56 | $57 | -$1 | $1 |
| 6 | $55 | $54 | $1 | $1 |
| 7 | $57 | $58 | -$1 | $1 |
| Totals | Sum: $9 |
Average Error = $9 / 7 = $1.29
Therefore, the average error in predicting the stock price is $1.29.
Why Use Absolute Values?
Using absolute values prevents positive and negative errors from canceling each other out. If you simply averaged the errors (without taking the absolute value), a model that consistently overestimates by a certain amount and underestimates by a similar amount could appear to have a very low average error, even though it's actually making significant mistakes.
Limitations of Average Error
While average error provides a general sense of accuracy, it doesn't tell you anything about the distribution of errors. For example, two models could have the same average error, but one might have more frequent small errors while the other has fewer, larger errors. Other metrics like Mean Squared Error (MSE) or Root Mean Squared Error (RMSE) might provide a more complete picture in some cases.
