Data collected on the yearly registrations for a Six Sigma seminar at the Qualit
ID: 354767 • Letter: D
Question
Data collected on the yearly registrations for a Six Sigma seminar at the Quality College are shown in the foowing table 10 1 Year Registrations (000) 5.0 5.00 500 500 10.0 9.00 800 1100 13.00 1200 1500 a) Calculate the forecasted registrations for years 2 through 12 using exponential smoothing, with a smocthing constant (a) of 0.35 and a starting forecast of 4.00 for year 1 fround your respanses to ane decimal place): 12 ear Forecast (000) 400 4647 4.8 6675 7.7 8 103 109 12.3 b) Mean absclute devistion based on the forecast developed using the exponential smoothing method (with a smoothing constant (x) 0.35 and a starting forecas ofF1-4.00) registrations (round your response to one decimal place)Explanation / Answer
a) Ft=(1-a)Ft-1+aFt-1
F2=0.65×4+0.35×5=2.6+1.75=4.4
F3=0.65×4.4+0.35×5= 2.86 + 1.75= 4.6
F4 =0.65×4.6+0.35×5=2.99+1.75= 4.7
F5=0.65×4.7+0.35×5=3.055+ 1.75=4.8
F6 = 0.65×4.8 + 0.35×10=6.6
F7= 0.65×6.6 + 0.35×9=7.4
F8= 0.65×7.4 + 0.35×8=7.6
F9= 0.65×7.6 + 0.35×11=8.8
F10= 0.65×8.8 + 0.35 × 13=10.3
F11= 0.65×10.3 + 0.35 ×13=10.9
F12 =0.65×10.9 + 0.35×15=12.3
b) Mean of the data= 7.2
Absolute Deviation from mean= |data-mean| are as follows:
3.2 2.8 2.6 2.5 2.4 0.6 0.2 0.4 1.6 3.1 3.7 5.1
Mean absolute Deviation = 3.2+2.8+2.6 +2.5.+2.4+0.6.+0.2+0.4+1.6+3.1+3.7+5.1/12
=2.4
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