Consider the following results from the last ten periods of student enrollment forecast by the Operations Management department chairman. Pe

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Consider the following results from the last ten periods of student enrollment forecast by the Operations Management department chairman. Period Forecast Actual 1 25 26 2 32 31 3 42 45 4 53 50 5 64 70 6 70 72 7 81 78 8 88 90 9 95 100 10 102 110 Determine the mean absolute percentage error (MAPE, round to two decimal places). Enter answer as decimal. (10% should be entered as .1)

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  1. Answer:

    MAPE = 2.33%

    Step-by-step explanation:

    The mean absolute percentage error (MAPE) can be determined by:

    MAPE = [tex]\frac{100}{n}[/tex] ∑[tex]|\frac{(Actual – Forecast)}{Actual} |[/tex]

    Given that:

                    periods are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

                  forecast are 25, 32, 42, 53, 64, 70, 81, 88, 95, 102

                      actual are 26, 31, 45, 50, 70, 72, 78, 90, 100, 110

    Thus, n = 10 and;

    ∑[tex]|\frac{(Actual – Forecast)}{Actual} |[/tex] = |[tex]\frac{(26 – 25)}{26}[/tex] + [tex]\frac{(31 – 32)}{31}[/tex] + [tex]\frac{(45 – 42)}{45}[/tex] + [tex]\frac{(50 – 53)}{50}[/tex] + [tex]\frac{(70 – 64)}{70}[/tex] + [tex]\frac{(72 – 70)}{72}[/tex] + [tex]\frac{(78-81)}{78}[/tex] + [tex]\frac{(90-88)}{90}[/tex] + [tex]\frac{(100-95)}{100}[/tex] + [tex]\frac{(110-102)}{110}[/tex]|

           = |0.0385 + (-0.0323) + 0.0667 + (-0.06) + 0.0857 + 0.0278 + (-0.0385) + 0.0222 + 0.05 + 0.07273|

          = 0.23283

    Therefore;

    MAPE = [tex]\frac{100}{10}[/tex] x 0.23283

              = 10 x 0.23283

              = 2.3283%

              = 2.33%

    The mean absolute percentage error = 2.33%

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