In: Statistics and Probability
Determine the magnitude of the seasonal ratio of the average quarter centered at that time period.
Quarterly Sales ($1,000,000s) for Turner Industries | ||||
Quarter | Year 1 | Year 2 | Year 3 | Average |
1 | 108 | 116 | 123 | 115.67 |
2 | 125 | 134 | 142 | 133.67 |
3 | 150 | 159 | 168 | 159 |
4 | 141 | 152 | 165 | 152.67 |
Average | 131 | 140.25 | 149.5 | 140.25 |
Centered | ||||||
Moving | Ratio to | Seasonal | ||||
t | Year | Quarter | Data | Average | CMA | Indexes |
1 | 1 | 1 | 108 | 0.849 | ||
2 | 1 | 2 | 125 | 0.963 | ||
3 | 1 | 3 | 150 | 132.000 | 1.136 | 1.131 |
4 | 1 | 4 | 141 | 134.125 | 1.051 | 1.057 |
5 | 2 | 1 | 116 | 136.375 | 0.851 | 0.849 |
6 | 2 | 2 | 134 | 138.875 | 0.965 | 0.963 |
7 | 2 | 3 | 159 | 141.125 | 1.127 | 1.131 |
8 | 2 | 4 | 152 | 143.000 | 1.063 | 1.057 |
9 | 3 | 1 | 123 | 145.125 | 0.848 | 0.849 |
10 | 3 | 2 | 142 | 147.875 | 0.960 | 0.963 |
11 | 3 | 3 | 168 | 1.131 | ||
12 | 3 | 4 | 165 | 1.057 | ||
Calculation of Seasonal Indexes | ||||||
1 | 2 | 3 | 4 | |||
1 | 1.136 | 1.051 | ||||
2 | 0.851 | 0.965 | 1.127 | 1.063 | ||
3 | 0.848 | 0.960 | ||||
mean: | 0.849 | 0.963 | 1.132 | 1.057 | 4.000 | |
adjusted: | 0.849 | 0.963 | 1.131 | 1.057 | 4.000 |
The graph is: