the mean absolute percentage error (mape) for the forecasts shown in the following table is:\n| month |…

the mean absolute percentage error (mape) for the forecasts shown in the following table is:\n| month | forecast demand | actual demand |\n| april | 110 | 100 |\n| may | 150 | 125 |\n| june | 160 | 170 |\n| july | 110 | 130 |\n| august | 150 | 180 |\nless than or equal to 5 percent.\nmore than 5 percent but less than or equal to 10 percent.\nmore than 10 percent but less than or equal to 15 percent.\nmore than 15 percent.

the mean absolute percentage error (mape) for the forecasts shown in the following table is:\n| month | forecast demand | actual demand |\n| april | 110 | 100 |\n| may | 150 | 125 |\n| june | 160 | 170 |\n| july | 110 | 130 |\n| august | 150 | 180 |\nless than or equal to 5 percent.\nmore than 5 percent but less than or equal to 10 percent.\nmore than 10 percent but less than or equal to 15 percent.\nmore than 15 percent.

Answer

Explanation:

Step1: Recall MAPE formula

$MAPE=\frac{1}{n}\sum_{i = 1}^{n}\left|\frac{A_i - F_i}{A_i}\right|\times100%$, where $A_i$ is actual value, $F_i$ is forecast - value and $n$ is number of data points. Here $n = 5$.

Step2: Calculate absolute percentage error for each month

  • April: $\left|\frac{100 - 110}{100}\right|\times100%=\left|\frac{- 10}{100}\right|\times100% = 10%$
  • May: $\left|\frac{125 - 150}{125}\right|\times100%=\left|\frac{-25}{125}\right|\times100% = 20%$
  • June: $\left|\frac{170 - 160}{170}\right|\times100%=\left|\frac{10}{170}\right|\times100%\approx5.88%$
  • July: $\left|\frac{130 - 110}{130}\right|\times100%=\left|\frac{20}{130}\right|\times100%\approx15.38%$
  • August: $\left|\frac{180 - 150}{180}\right|\times100%=\left|\frac{30}{180}\right|\times100%\approx16.67%$

Step3: Calculate MAPE

$MAPE=\frac{10%+20% + 5.88%+15.38%+16.67%}{5}=\frac{67.93%}{5}=13.59%$

Answer:

more than 10 percent but less than or equal to 15 percent.