Question

Storrs Cycles has just started selling the new Cyclone mountain​ bike, with monthly sales as shown in the table.

                                                              

Month	Jan	Feb	Mar	Apr
Sales	400	372	418	375

​a) Based on the given monthly sales​ data, it can be said that there is

not a strong

linear trend in sales over time.

​b) First,​ co-owner Bob Day wants to forecast by exponential smoothing by initially setting​ February's forecast equal to​ January's sales with

α

​=

0.20.

Using the forecasting​ method, Bob's forecast for the month of May is ​(round your response to two decimal​ places):

Month	Sales	Forecast
Jan	400	−
Feb	372	400.00
Mar	418	394.40
Apr	375	399.12
May	−	394.29394.29

​Second, co-owner Sherry Snyder wants to forecast using a​ three-period moving average. The forecast for the month of May is ​(round your response to two decimal​ places).

Month	Sales	Forecast
Jan	400	−
Feb	372	−
Mar	418	−
Apr	375	396.67
May	−	388.33388.33

​c) Assume that​ May's actual sales figure turns out to be

400.

For the forecast developed by Bob using exponential​ smoothing, the mean absolute deviation​ (MAD) =

20.3620.36

sales ​(round your response to two decimal​ places).

Assume that​ May's actual sales figure turns out to be . For the forecast developed by Sherry using a​ 3-month moving​ average, the mean absolute deviation​ (MAD) = _______sales ​(round your response to two decimal​ places). ​d) Based on the above​ calculations, the forecast approach used by_____ is better.

Answer 1

​a) Based on the given monthly sales​ data, it can be said that there is not a strong linear trend in sales over time.

Statement is TRUE, considering that sales are not always increasing with time hence is not a strong linear here.

​b) First,​ co-owner Bob Day wants to forecast by exponential smoothing by initially setting​ February's forecast equal to​ January's sales with

α=0.20

As per exponential smoothing forecast, Forecast = α*Actual of previous period + (1- α)* Forecast of previous period

Month	Sales	Forecast
Jan	400	−
Feb	372	400
Mar	418	372*0.2+(1-0.2)*400=394.4
Apr	375	418*0.2+(1-0.2)*394.4=399.12
May	−	375*0.2+(1-0.2)*399.12=394.296

​Second, co-owner Sherry Snyder wants to forecast using a​ three-period moving average. The forecast for the month of May is ​(round your response to two decimal​ places).

As per three period moving average Forecast = (Actuals for last three periods)/3

Month	Sales	Forecast
Jan	400	−
Feb	372
Mar	418
Apr	375	(400+372+418)/3=396.67
May	−	(372+418+375)/3=388.33

​c) Assume that​ May's actual sales figure turns out to be

400.

mean absolute deviation​ (MAD) = | (Actual - Forecast)|/ n

For the forecast developed by Bob using exponential​ smoothing, the mean absolute deviation​ (MAD) as calculated below

Month	Sales	Forecast	Deviation	Abs Dev.
Jan	400	−
Feb	372	400	-28	28
Mar	418	372*0.2+(1-0.2)*400=394.4	23.6	23.6
Apr	375	418*0.2+(1-0.2)*394.4=399.12	-24.12	24.12
May	400	375*0.2+(1-0.2)*399.12=394.296	5.704	5.704
			MAD	20.356

Assume that​ May's actual sales figure turns out to be 400. For the forecast developed by Sherry using a​ 3-month moving​ average, the mean absolute deviation​ (MAD) as calculated below

Month	Sales	Forecast	Deviation	Abs Dev.
Jan	400	−
Feb	372
Mar	418
Apr	375	(400+372+418)/3=396.67	-21.67	21.67
May	400	(372+418+375)/3=388.33	11.67	11.67
			MAD	16.67

d) Based on the above​ calculations, the forecast approach used by "three-period moving average" is better.

Because MAD is lower for forecast as per three-period moving average compared to exponential smoothing.

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