To findout the seasonal indices for each seasons,we need to find out the following for each year:
Total attendeance for the year = Sum of the attendance of all the seasons in that year
average quarterly attendance for the year = Total attendance for the year / 4
Seasonal index for each seasons in the year = Demand for the season of the year/ Average quarterly demand for the year
Using the above formulas the following calculations for year 1,year 2 and year 3 are made:
For year 1:
- Total attendance = (68+89+168+75) = 400
- Average quarterly attendance = 400/4 = 100
- Seasonal index for winter year 1 = 68/100 = 0.68
- Seasonal index for Spring year 1 = 89/100 = 0.89
- Seasonal index for summer year 1 = 168/100 = 1.68
- Seasonal index for fall year 1 = 75/100 = 0.75
For year 2 :
- Total attendance = 63+82+120+54 = 319
- Average quarterly attendance = 319/4 = 79.75
- Seasonal inxed for winter year 2 = 63/79.75 = 0.790
- Seasonal index for Spring year 2 = 82/79.75 = 1.028
- Seasonal index for Summer year 2 = 120/79.75 = 1.505
- Seasonal index for fall year 2 = 54/79.75 = 0.677
For year 3 :
- Total attendance = 99+151+207+99 = 556
- Average quarterly attendance = 556/4 = 139
- Seasonal inxed for winter year 3 = 99/139 = 0.712
- Seasonal index for Spring year 3 = 151/139 = 1.086
- Seasonal index for Summer year 3 = 207/139 = 1.489
- Seasonal index for fall year 3 = 99/139 = 0.712
Seasonal index for Winter = (Seasonal index for winter year 1+seasonal index for winter year 2+Seasonal index for winter year 3) / Number of years
= (0.68 + 0.790 + 0.712) / 3
= 0.727
Seasonal index for Spring =(Seasonal index for spring year 1+seasonal index for spring year 2+seasonal index for spring year 3) / Number of year
=(0.89 + 1.028 + 1.086) / 3
= 1.001
Seasonal index for Summer =(Seasonal index for summer year 1+seasonal index for summer year 2+seasonal index for summer year 3) / Number of year
= (1.68 + 1.505 + 1.489) / 3
= 1.558
Seasonal index for Fall =(Seasonal index for fall year 1+seasonal index for fall year 2+seasonal index for fall year 3) / Number of year
= (0.75 + 0.677 + 0.712) / 3
= 0.713
So the final answer is:
Season Index
Winter 0.727
Spring 1.001
Summer 1.558
Fall 0.713
