Question 2. The quarterly sales data (number of copies sold) for a college textb

Question

Question 2.

The quarterly sales data (number of copies sold) for a college textbook over the past 3 years are as follows in Table 2:

Table 2: Quarterly sales

Quarter

Year 1

Year 2

Year 3

1

16

18

18

2

9

9

11

3

26

29

29

4

25

23

26

A. Compute seasonal indexes for the 4 quarters.

B. When does the textbook publisher experience the largest seasonal index? Does this result appear to be reasonable? Explain.

C. Using the information on seasonality, show a 4-quarter moving average values for this time series and forecast for the 1st quarter of the 4th year.

Quarter

Year 1

Year 2

Year 3

1

16

18

18

2

9

9

11

3

26

29

29

4

25

23

26

Explanation / Answer

First calculate seasonal index for quarters in each years, then to get the overall seasonal index for that quarter, take the average of all seasonal index. Explained below.

First calculate all seasonal index of Year as shown in table below

For Q1, Seasonal Index = 16 / 76 = 0.21

Similarly calculate for year 2 and 3 as below

Now Quarter 1 seasonal index = average of all Q1 indexes = (0.84 + 0.91 + 0.86 ) / 3 = 0.87

Similarly all quarters index can be calculated, and results are shown below

B. Largest index is experienced in quarter 3. After summer vacation, when school starts, maximum number of students have to buy new text books. This is the primary reason for high book sales in quarter 3.

C. First find the desesasonalized data by dividing sales by its seasonal index.

Quarter Year 1 Seasonal Index 1 16 0.84 2 9 0.47 3 26 1.37 4 25 1.32 Total 19

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