7. Sampling Distributions & Confidence Intervals: Mean
Introduction to Confidence Intervals
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Given the following forecast and actual demand data for four periods: Forecasts = [100, 120, 130, 110], Actual Demands = [110, 115, 125, 120], what is the Mean Absolute Percentage Error (MAPE) for these periods?
A
6.82%
B
5.50%
C
8.25%
D
10.00%
Verified step by step guidance1
Step 1: Understand the formula for Mean Absolute Percentage Error (MAPE). MAPE is calculated as: \( \text{MAPE} = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{\text{Actual}_i - \text{Forecast}_i}{\text{Actual}_i} \right| \times 100 \), where \( n \) is the number of periods, \( \text{Actual}_i \) is the actual demand for period \( i \), and \( \text{Forecast}_i \) is the forecasted demand for period \( i \).
Step 2: Calculate the absolute percentage error for each period. For each period \( i \), compute \( \left| \frac{\text{Actual}_i - \text{Forecast}_i}{\text{Actual}_i} \right| \times 100 \). For example, for the first period: \( \left| \frac{110 - 100}{110} \right| \times 100 \). Repeat this calculation for all four periods.
Step 3: Sum up the absolute percentage errors obtained in Step 2. Add the values calculated for each period to get the total absolute percentage error.
Step 4: Divide the total absolute percentage error by the number of periods (\( n = 4 \)) to find the mean absolute percentage error. Use the formula \( \text{MAPE} = \frac{\text{Total Absolute Percentage Error}}{n} \).
Step 5: Interpret the result. The MAPE value represents the average percentage error between the forecasted and actual demand over the four periods. Compare the calculated MAPE to the given options (6.82%, 5.50%, 8.25%, 10.00%) to identify the correct answer.
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