What is the mean absolute percentage error based on the following data? Period Actual Forecast 1 173 166.7 2 177 183 3 180 174.7 4 151 163.2 5 168 155.6 6 184 187.6 7 198 192.9 8... What is the mean absolute percentage error based on the following data? Period Actual Forecast 1 173 166.7 2 177 183 3 180 174.7 4 151 163.2 5 168 155.6 6 184 187.6 7 198 192.9 8 191 194.6 9 167 149.8 10 177 195.2
Understand the Problem
The question asks to calculate the Mean Absolute Percentage Error (MAPE) given a table of actual and forecasted class enrollments over 10 periods. MAPE is calculated as the average of the absolute percentage errors for each period. This involves finding the absolute difference between the actual and forecasted values, dividing by the actual value, multiplying by 100 to get the percentage error for each period, and then averaging these percentage errors.
Answer
$11.35\%$
Answer for screen readers
$11.35%$
Steps to Solve
- Calculate the absolute difference between actual and forecast for each period
For each period, subtract the forecasted value from the actual value, and take the absolute value. For example, for period 1: $|18 - 23| = |-5| = 5$. We repeat this for all 10 periods.
- Calculate the percentage error for each period
Divide the absolute difference by the actual value for each period, and then multiply by 100. For example, for period 1: $(5 / 18) * 100 = 27.78%$.
- Sum the percentage errors
Add all of the percentage errors calculated in the previous step.
- Calculate the Mean Absolute Percentage Error (MAPE)
Divide the sum of percentage errors by the number of periods (which is 10 in this case) to get the MAPE.
The table below shows the step by step calculation:
| Period | Actual | Forecast | Absolute Difference | Percentage Error (%) |
|---|---|---|---|---|
| 1 | 18 | 23 | $ | 18-23 |
| 2 | 21 | 19 | $ | 21-19 |
| 3 | 23 | 18 | $ | 23-18 |
| 4 | 22 | 24 | $ | 22-24 |
| 5 | 20 | 21 | $ | 20-21 |
| 6 | 17 | 16 | $ | 17-16 |
| 7 | 19 | 19 | $ | 19-19 |
| 8 | 25 | 22 | $ | 25-22 |
| 9 | 27 | 26 | $ | 27-26 |
| 10 | 16 | 19 | $ | 16-19 |
| Sum | 113.46 |
$MAPE = \frac{113.46}{10} = 11.346$
$11.35%$
More Information
The Mean Absolute Percentage Error (MAPE) is a measure of the accuracy of a forecasting method in statistics. It measures the average magnitude of the errors in a set of forecasts, without considering their direction. It is useful for comparing the accuracy of different forecasting methods.
Note: The answer is rounded to two decimal places.
Tips
A common mistake is to calculate the percentage error using the forecast value as the denominator instead of the actual value. It's important to remember that MAPE is calculated based on the actual values, as it reflects the percentage deviation from what actually happened.
Also, make sure to take the absolute value of the difference between the actual and predicted values before calculating the percentage error.
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