Calculate The Mean Absolute Percentage Error for The Following Data

The Mean Absolute Percentage Error (MAPE) is a measure of prediction accuracy of a forecasting method in statistics. It measures the accuracy of each forecast as a percentage and then calculates the average of these percentages.

What is Mean Absolute Percentage Error (MAPE)?

Mean Absolute Percentage Error (MAPE) is a common metric used to evaluate the accuracy of forecasts. It provides a percentage-based measure of the average absolute error between actual and forecasted values.

MAPE is calculated by taking the absolute difference between each actual value and its corresponding forecast, dividing by the actual value, and then averaging these percentages. The result is expressed as a percentage.

MAPE is particularly useful when you want to compare forecast accuracy across different time series with different scales. However, it has some limitations, such as being undefined when actual values are zero and potentially misleading when actual values are close to zero.

How to Calculate MAPE

To calculate MAPE, follow these steps:

For each data point, calculate the absolute percentage error: (|Actual - Forecast| / Actual) × 100
Sum all the absolute percentage errors
Divide the sum by the number of data points
The result is the MAPE

MAPE Formula:

MAPE = (1/n) × Σ(|(Actual_i - Forecast_i) / Actual_i|) × 100

Where:

n = number of data points
Actual_i = actual value for period i
Forecast_i = forecasted value for period i

Interpreting MAPE Results

MAPE results are interpreted as percentages. A lower MAPE indicates better forecast accuracy. Common benchmarks for MAPE include:

0-15%: Excellent
15-25%: Good
25-50%: Reasonable
50% or higher: Poor

However, these benchmarks are general guidelines and may not apply to all forecasting scenarios. Always consider the context and specific requirements of your forecasting task.

Worked Example

Let's calculate MAPE for a simple example with 5 data points:

Period	Actual	Forecast
1	100	110
2	200	190
3	300	330
4	400	380
5	500	520

Calculating the absolute percentage errors:

Period 1: (|100-110|/100) × 100 = 10%
Period 2: (|200-190|/200) × 100 = 5%
Period 3: (|300-330|/300) × 100 = 10%
Period 4: (|400-380|/400) × 100 = 5%
Period 5: (|500-520|/500) × 100 = 4%

Sum of absolute percentage errors: 10 + 5 + 10 + 5 + 4 = 34%

MAPE = 34% / 5 = 6.8%

This result indicates a good forecast accuracy according to the common benchmarks.

Frequently Asked Questions

What is the difference between MAPE and RMSE?

MAPE and RMSE (Root Mean Square Error) are both measures of forecast accuracy, but they have different characteristics. MAPE provides a percentage-based measure of average absolute error, while RMSE provides a measure of the average magnitude of the errors in the same units as the data. MAPE is often preferred when comparing forecasts across different scales, while RMSE is more sensitive to large errors.

When should I use MAPE instead of other accuracy measures?

MAPE is particularly useful when you want to compare forecast accuracy across different time series with different scales. It provides a percentage-based measure that is easy to interpret. However, it has some limitations, such as being undefined when actual values are zero and potentially misleading when actual values are close to zero.

How can I improve my forecast accuracy if MAPE is high?

If your MAPE is high, consider the following strategies to improve forecast accuracy:

Use more sophisticated forecasting methods
Incorporate additional relevant variables
Improve data quality and availability
Consider using ensemble forecasting methods
Regularly review and update your forecasting models