Question

Calculating Forecast Error Measures The following table shows the actual sales of upholstered chairs for a furniture manufacturer and the forecasts made for each of the last 8 months. Calculate CFE, MSE, a, MAD, and MAPE for this product Month, Demand, D Forecast Error E Error, Squared, E Absolute Error, Absolute Percent Error, (END(100) 200 225 -25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 270 290 -20 400 20 74 5 230 250 -20 400 20 8.7 260 20 20 7.7 240 400 19.0 7 210 250 -40 1,600 40 8 275 240 35 1,225 35 12.7 Total -15 5,275 195 81.3% st

Please solve for the standard deviation step by step.

Answer 1

CFE = cumulative forecast error = -15

MSE = Sum Err, Squared/ 8 = 5275/8 = 659.375

MAD = Sum of absolute error/8 = 195/8 = 24.375

MAPE = Sum of Absolute percent error/8 = 81.3%/8 = 10.1625%

Variance =[Sum (Error(t) - (Average Error)]/(n-1) where t = period and n = number of observations = 8 here. Average Error = -15/8 = -1.875

Variance = ((-25 - (-1.875))^2 + (20 - (-1.875))^2 + (15 - (-1.875))^2 + (-20 - (-1.875))^2 + (-20 - (-1.875))^2 + (20 - (-1.875))^2 + (-40 - (-1.875))^2 + (35 - (-1.875))^2)/(8-1)

= (534.765625+478.515625+284.765625+328.515625+328.515625+478.515625+1453.515625+1359.765625)/7

= 749.5535714

Standard deviation = sqrt(variance) = sqrt(749.5535714) = 27.378