QCE General Maths · Free Worksheet
Time Series Analysis
Smoothing data with moving averages and finding seasonal components — practice questions for QCE Mathematics General, Unit 3.
What's inside
- A short recap of the method before the questions start
- Practice questions ordered from easiest to hardest
- Space to show full working, plus an answer key
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Sample questions
Question 1
Calculate the 3-point moving averages for the time series 12, 15, 18, 14, 20 (centred at the 2nd, 3rd and 4th values).
Show worked solution
MA₂ = (12 + 15 + 18) ÷ 3 = 45 ÷ 3 = 15. MA₃ = (15 + 18 + 14) ÷ 3 = 47 ÷ 3 ≈ 15.67. MA₄ = (18 + 14 + 20) ÷ 3 = 52 ÷ 3 ≈ 17.33.
Question 2
Quarterly sales for Q2 were $55,000, with an underlying trend value of $48,000. Using the additive model (seasonal = actual − trend), find the seasonal component for Q2.
Show worked solution
Seasonal component = actual − trend = 55 − 48 = $7,000 above trend.
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