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Time series data is collected at regular intervals over time. Moving averages smooth out short-term fluctuations so you can identify the underlying trend. This is tested on all three Edexcel GCSE papers.
| Term | Definition |
|---|---|
| Time series | A set of data collected at regular time intervals |
| Trend | The general direction of the data over time (upward, downward, or level) |
| Seasonal variation | A pattern that repeats at regular intervals (e.g. quarterly, monthly) |
| Moving average | The mean of a fixed number of consecutive data points, recalculated as you move along the series |
| n-point moving average | The average of n consecutive values |
A time series graph has:
Ice cream sales (£000s) recorded over 8 quarters:
| Quarter | Q1 2023 | Q2 2023 | Q3 2023 | Q4 2023 | Q1 2024 | Q2 2024 | Q3 2024 | Q4 2024 |
|---|---|---|---|---|---|---|---|---|
| Sales | 12 | 28 | 35 | 15 | 14 | 32 | 40 | 18 |
Describe the trend and the seasonal variation.
Solution: Plot each quarter against its sales value and join with straight lines.
Moving averages smooth out seasonal variation to reveal the underlying trend.
Using the data from Worked Example 1, calculate all the 4-point moving averages.
Solution: For quarterly data, use a 4-point moving average (because there are 4 quarters in a year).
| Values used | Moving average | Plotted between |
|---|---|---|
| Q1–Q4 2023 | 22.5 | Q2–Q3 2023 |
| Q2 2023–Q1 2024 | 23.0 | Q3–Q4 2023 |
| Q3 2023–Q2 2024 | 24.0 | Q4 2023–Q1 2024 |
| Q4 2023–Q3 2024 | 25.25 | Q1–Q2 2024 |
| Q1–Q4 2024 | 26.0 | Q2–Q3 2024 |
Each moving average is plotted at the midpoint of the period it covers. For a 4-point moving average this falls between the 2nd and 3rd of the four points. Join the MA points to show the trend line.
Observation: The moving averages increase from 22.5 to 26.0 — confirming an overall upward trend.
Monthly visitors at a museum: 120, 150, 180, 130, 160, 190, 140. Calculate the 3-point moving averages.
Solution: Use a 3-point moving average (odd, so plot at the middle value).
The MAs rise from 150 to 163.3 — an upward trend.
A shop calculates 4-point moving averages: 50, 52, 54, 56. Describe the trend.
Solution: The moving averages increase steadily by 2 each time, showing a steady upward trend in the underlying data.
Seasonal effect at a given time point = actual value − trend value.
Suppose the trend value at Q3 2023 is 24, and actual Q3 2023 sales are 35. What is the seasonal effect for Q3?
Solution: Seasonal effect = actual − trend = 35 − 24 = +11 (Q3 is 11 above the trend).
If Q3 2024 actual sales are 40 and the trend value at Q3 2024 is 27, the seasonal effect is 40 − 27 = +13.
Average Q3 seasonal effect ≈ (11 + 13) ÷ 2 = +12 (used for predictions).
Once you have a trend line (from moving averages), you can extend it to make predictions.
Predicted value = trend estimate ± seasonal effect
A shop's 4-point moving averages for umbrella sales are 60, 61.25, 62.5, 63.75, 65. Q1 sales are typically 22 above the trend (seasonal effect for Q1 = +22). The trend for Q1 2024 is estimated at 66.25.
Predict actual Q1 2024 sales.
Solution: Predicted sales = trend + seasonal effect = 66.25 + 22 = ≈ 88 umbrellas.
Caution: Predictions assume the trend and seasonal pattern continue. The further into the future you predict, the less reliable the estimate.
The table shows the number of umbrellas sold at a shop each quarter.
| Quarter | Q1 2022 | Q2 2022 | Q3 2022 | Q4 2022 | Q1 2023 | Q2 2023 | Q3 2023 | Q4 2023 |
|---|---|---|---|---|---|---|---|---|
| Sales | 80 | 40 | 30 | 90 | 85 | 45 | 35 | 95 |
(a) Calculate the 4-point moving averages. (b) Describe the trend. (c) Describe the seasonal variation. (d) Predict the sales for Q1 2024.
Solution:
(a)
(b) The moving averages increase from 60 to 65 — a slight upward trend in umbrella sales.
(c) Sales are highest in Q4/Q1 (autumn/winter) and lowest in Q3 (summer). This makes sense because people buy more umbrellas in wet months.
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