Trend Lines and Seasonal Variation
Master Trend Lines and Seasonal Variation for GCSE Statistics with this free worksheet and full mark scheme — Higher tier exam-style questions with worked answers for AQA and Edexcel. A trend line through the moving averages shows the overall trend, and seasonal variation is the difference from it.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.
This is a Higher tier only topic, so there's no Foundation paper — only the Higher worksheet and mark scheme below.
Topic overview
A trend line drawn through a moving average shows the underlying direction of a time series, and seasonal variation can then be measured against it. This is a Higher-only topic.
The trend line is drawn through the plotted moving averages, not through the original data points, because the moving averages have already had seasonal variation smoothed out.
Seasonal variation for any point is calculated as actual value minus trend value. A positive result means the actual value was above trend for that season; a negative result means below. The mean seasonal variation for a given season is found by averaging its variations across cycles, and this is used to make predictions: predicted value = trend value + mean seasonal variation.
Revision notes
Drawing the trend line
Draw the line of best fit through the plotted moving averages, not the original data points.
The moving averages have already had seasonal variation smoothed out, so they show the underlying trend directly.
Calculating seasonal variation
Seasonal variation \(=\) actual value \(-\) trend value.
A positive result means the actual value was above the trend for that season; negative means below. Calculate it for each point where a trend value exists.
Predicting future values
Extend the trend line to read the trend value for the future period.
Then predicted value \(=\) trend value \(+\) mean seasonal variation for that season. The mean seasonal variation is found by averaging that season's variations across the cycles available.
Key points
- The trend line goes through the moving averages.
- Moving averages have seasonality removed.
- Seasonal variation = actual − trend.
- A positive variation means above trend.
- Mean seasonal variation averages across cycles.
- Prediction = trend value + mean seasonal variation.
Worked examples
Example 1
An actual value is 340 and the trend value is 310. Work out the seasonal variation. [2 marks]
Working
Example 2
A trend value is 480 and the mean seasonal variation for that quarter is \(-25\). Work out the predicted value. [2 marks]
Working
Example 3
Explain why the trend line is drawn through the moving averages rather than the original data. [2 marks]
Working
Common mistakes
Drawing the trend line through the raw data.
It goes through the moving averages, which are already smoothed.
Subtracting the wrong way round.
Seasonal variation is actual minus trend, so it can be negative.
Forgetting the sign of the seasonal variation.
A negative variation must be added as a negative when predicting.
Using a single season's variation rather than the mean.
Average that season's variations across the cycles available.
Exam tips
- Draw the trend line through the moving averages.
- Subtract trend from actual, keeping the sign.
- Use the mean seasonal variation when predicting.
- Remember this is a Higher-only topic.
Key terms
- Trend line
- A line of best fit through the moving averages.
- Seasonal variation
- Actual value minus trend value.
- Mean seasonal variation
- The average variation for a given season.
- Prediction
- Trend value plus mean seasonal variation.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.