Using the data below, what is the value of the Mean absolute percent error (MAPE)?

Week

Time Series Value

Forecast

1

17

7.00

2

25

32.00

3

14

12.00

4

23

21.00



To calculate the **Mean Absolute Percentage Error (MAPE)**, we use the following formula:

\[
\text{MAPE} = \frac{1}{n} \sum_{t=1}^{n} \left| \frac{A_t - F_t}{A_t} \right| \times 100
\]

Where:
- \(A_t\) is the actual value at time \(t\),
- \(F_t\) is the forecast value at time \(t\),
- \(n\) is the number of observations.

Let's calculate the MAPE step by step:

**Given Data:**
- Week 1: Actual = 17, Forecast = 7.00
- Week 2: Actual = 25, Forecast = 32.00
- Week 3: Actual = 14, Forecast = 12.00
- Week 4: Actual = 23, Forecast = 21.00

### Step 1: Calculate the absolute percentage error for each week

\[
\text{Error}_1 = \left| \frac{17 - 7}{17} \right| \times 100 = \left| \frac{10}{17} \right| \times 100 \approx 58.82\%
\]
\[
\text{Error}_2 = \left| \frac{25 - 32}{25} \right| \times 100 = \left| \frac{-7}{25} \right| \times 100 = 28.00\%
\]
\[
\text{Error}_3 = \left| \frac{14 - 12}{14} \right| \times 100 = \left| \frac{2}{14} \right| \times 100 \approx 14.29\%
\]
\[
\text{Error}_4 = \left| \frac{23 - 21}{23} \right| \times 100 = \left| \frac{2}{23} \right| \times 100 \approx 8.70\%
\]

### Step 2: Calculate the average of these absolute percentage errors (MAPE)

\[
\text{MAPE} = \frac{58.82 + 28.00 + 14.29 + 8.70}{4} \approx \frac{109.81}{4} \approx 27.45\%
\]

Thus, the **MAPE** is approximately **27.45%**.

Would you like further details on the calculations or clarifications?

Here are some related questions to explore:

1. How does MAPE compare to other error metrics like MAE and RMSE?
2. What are the advantages and disadvantages of using MAPE in forecasting?
3. How can the size of errors affect MAPE's interpretation?
4. What happens to MAPE if one of the actual values is zero?
5. How does MAPE behave with positive vs. negative forecast deviations?

**Tip:** MAPE is highly sensitive to small actual values, which can lead to inflated percentage errors. Consider using other metrics when dealing with data near zero.

Using the data below, what is the value of the Mean absolute percent error (MAPE)?

Week

Time Series Value

Forecast

1: 17 (Actual), 7.00 (Forecast)
2: 25 (Actual), 32.00 (Forecast)
3: 14 (Actual), 12.00 (Forecast)
4: 23 (Actual), 21.00 (Forecast)

Learn how to calculate the Mean Absolute Percentage Error (MAPE) using time series data. This step-by-step guide includes data on forecast and actual values for four weeks, demonstrating how to apply the MAPE formula to measure forecasting accuracy.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation