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How do you find the mean absolute percentage deviation?

Published in Error Calculation 3 mins read

The mean absolute percentage deviation (MAPD), often referred to as mean absolute percentage error (MAPE), is found by calculating the average of the absolute percentage differences between predicted and actual values.

Here’s a step-by-step guide to calculate it:

Calculating Mean Absolute Percentage Deviation (MAPD)

  1. Calculate the Residuals:

    • For each data point, find the difference between the actual value and the predicted value. This is called the residual.

  2. Take the Absolute Value:

    • Take the absolute value of each residual. This turns negative residuals into positive ones. We want to measure the magnitude of the error, not its direction.

  3. Calculate Percentage Error:

    • For each data point, divide the absolute residual by the original data point, and then multiply by 100. This results in the percentage error for each point.
    • As the reference states, "Once we calculate the absolute value of a residual, we divide this value by the original data point and multiply by 100 to figure out how far off our model is as a percentage."

  4. Sum the Percentage Errors:

    • Add up all of the calculated percentage errors.

  5. Calculate the Mean:

    • Divide the sum of the percentage errors by the total number of data points. This provides the average percentage error.

Formula for MAPD

The MAPD can be expressed by the following formula:

MAPD = (1/n) * Σ |(Actual - Predicted) / Actual| * 100

Where:

  • n is the number of data points.
  • Σ is the summation symbol (summing across all data points).
  • Actual is the original data value.
  • Predicted is the modeled/forecasted value.

Example Calculation

Let's consider a simplified dataset with the following values:

Data Point Actual Value Predicted Value
1 50 55
2 100 90
3 75 85

Following the above steps:

  1. Calculate Residuals:

    • Data Point 1: 50 - 55 = -5
    • Data Point 2: 100 - 90 = 10
    • Data Point 3: 75 - 85 = -10

  2. Absolute Residuals:

    • Data Point 1: |-5| = 5
    • Data Point 2: |10| = 10
    • Data Point 3: |-10| = 10

  3. Percentage Errors:

    • Data Point 1: (5/50) * 100 = 10%
    • Data Point 2: (10/100) * 100 = 10%
    • Data Point 3: (10/75) * 100 = 13.33%

  4. Sum of Percentage Errors:

    • 10% + 10% + 13.33% = 33.33%

  5. Mean Percentage Error:

    • 33.33% / 3 = 11.11%

Therefore, the mean absolute percentage deviation (MAPD) for this dataset is approximately 11.11%.

Key Takeaways

  • MAPD expresses the accuracy of a model as a percentage error.
  • It is often used when evaluating the performance of forecasting models.
  • It’s simple to calculate and understand.
  • MAPD is beneficial because it shows the error in relation to the original data point, rather than as an absolute difference.

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