📍 Scene Setup
It's the last working day of the financial year at Coastal Bay Resort. The automated staffing system locks at midnight and won't accept changes until April. Before it locks, the General Manager needs to approve next year's seasonal workforce plan, and the plan can only be submitted once all six seasonal index calculations are signed off.
The sun is setting. You've got the two-year visitor dataset in front of you. Six approvals stand between you and the exit.
📊 Coastal Bay Resort, Visitor Data (hundreds)
Season
Year 1
Year 2
Season Mean
☀️ Summer
140
168
154
🍂 Autumn
100
120
110
❄️ Winter
60
72
, (you'll calculate)
🌸 Spring
100
120
110
Total
400
480
Grand total: 880 · Overall mean: 110
Already confirmed: SISummer = 1.4 · SIAutumn = 1.0 · SISpring = 1.0
Overall mean = 110 · 4-season sum rule: all four SIs must add to 4.0
1
Approval 1, The Sum Rule
Three seasonal indices have been confirmed: Summer = 1.4, Autumn = 1.0, Spring = 1.0.
Using the rule that all four seasonal indices must sum to 4.0, what is the seasonal index for Winter?
This is a quick check before you calculate, the sum rule can always be used to find a missing index.
💡 All four SIs add to 4.0. You know three of them: 1.4 + 1.0 + 1.0 = 3.4. What's left?
✅ Approval 1 signed. SIWinter = 0.6, winter is 40% below the annual average.
2
Approval 2, Winter Season Mean
Winter visitor numbers were 60 (Year 1) and 72 (Year 2). Calculate the winter season mean.
Average the two winter values. This is the mean winter figure across both years, used to calculate the seasonal index.
💡 Season mean = (Year 1 winter + Year 2 winter) ÷ 2 = (60 + 72) ÷ 2
✅ Approval 2 signed. Winter season mean = 66 hundred visitors.
3
Approval 3, Calculate Winter SI
The winter season mean is 66. The overall mean is 110.
Calculate the seasonal index for Winter.
SI = season mean ÷ overall mean. This should match what you found using the sum rule in Step 1 · a good double-check!
💡 SI = season mean ÷ overall mean = 66 ÷ 110. Enter the decimal.
✅ Approval 3 signed. SI = 0.6, confirmed both ways!
4
Approval 4, Deseasonalise
Year 2 winter had 72 hundred visitors. The winter seasonal index is 0.6.
Calculate the deseasonalised value for Year 2 winter.
Deseasonalising removes the seasonal effect. If you remove the "winter discount", what is the underlying trend value this represents?
💡 Deseasonalised = actual ÷ SI. You're removing the seasonal effect, so you divide. 72 ÷ 0.6 = ?
✅ Approval 4 signed. Deseasonalised = 120. The true trend says 12,000 visitors, winter just makes it look like 7,200.
5
Approval 5, Make the Forecast
The trend line predicts that the underlying value for next winter will be 125 hundred visitors.
Using the winter seasonal index of 0.6, calculate the seasonally adjusted forecast for next winter.
Forecasting adds the seasonal effect back in. You know it's winter, so the actual visitors will be lower than the trend value, multiply by the SI.
💡 Forecast = trend value × SI. You're adding the seasonal effect back in, so multiply. 125 × 0.6 = ?