The seasonal indices for the number of bathing suits sold at a surf shop are given in thetable below. The number of bathing suits sold one summer is 432. The deseasonalised number isclosest to:

Question

BlackTom AI · Accepted Answer

Deseasonalising with a multiplicative seasonal index means you divide the observed value by the seasonal index for that period. The relevant knowledge: seasonal indices (multiplicative model) scale the underlying (deseasonalised) level up or down; to recover the underlying level you divide the observed value by the seasonal index.

1. Knowledge points and concepts
- Multiplicative seasonal model: Observed = Deseasonalised × Seasonal index.
- Therefore Deseasonalised = Observed ÷ Seasonal index.
- From the table the Summer seasonal index = 1.8.

2. Step-by-step reasoning and calculation
- Observed number in summer = 432.
- Seasonal index for summer = 1.8.
- Deseasonalised = 432 ÷ 1.8.
- Compute: 432 ÷ 1.8 = (432 × 10) ÷ (1.8 × 10) = 4320 ÷ 18.
- Now divide: 4320 ÷ 18 = 240.

3. Intermediate steps shown
- Multiply numerator and denominator by 10 to remove the decimal: 432/1.8 = 4320/18.
- Long division: 18 × 240 = 4320, so result = 240.

4. Why the correct answer is correct
- Because dividing the observed summer sales (432) by the summer seasonal factor (1.8) removes the seasonal effect, yielding the underlying (deseasonalised) value of 240.

5. Why the other options are incorrect
- a. 540 is larger than the observed value and would imply dividing by a seasonal index < 1 (not the case here).
- b. 432 would be correct only if the seasonal index were 1 (no seasonality), but the summer index is 1.8.
- d. 778 (≈777.6) equals 432 × 1.8, which is the result of incorrectly multiplying by the index instead of dividing.

Conclusion: The deseasonalised number is 240, matching option c. 240.

The seasonal indices for the number of bathing suits sold at a surf shop are given in thetable below. The number of bathing suits sold one summer is 432. The deseasonalised number isclosest to:Single choice

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