Moving Averages
Revise Moving Averages for GCSE Statistics with this free worksheet and full mark scheme — Higher tier exam-style questions with worked answers for AQA and Edexcel. Moving averages smooth out short-term fluctuations in a time series to reveal the underlying trend.
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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 moving average smooths a time series by averaging groups of consecutive values, making the underlying trend visible. This is a Higher-only topic.
The number of values averaged should match the cycle length. Quarterly data uses a four-point moving average, because a full cycle is four quarters. Monthly data with an annual cycle uses a twelve-point moving average.
Each moving average is calculated by taking the mean of that group of values, then moving the group forward by one position and repeating. Because the first and last values cannot be at the centre of a complete group, there are fewer moving averages than original data points, and they are plotted at the centre of each group.
Revision notes
Choosing the number of points
Match it to the cycle length in the data.
Quarterly data with an annual cycle uses a four-point moving average. Monthly data with an annual cycle uses twelve points. Using the wrong number fails to remove the seasonal variation.
Calculating the moving averages
Take the mean of the first group of values, then move the group forward one position and repeat.
For a four-point moving average of 12, 16, 20 and 24: \(\frac{12 + 16 + 20 + 24}{4} = 18\). The next uses values two to five.
Plotting them
Each moving average is plotted at the centre of the group it came from.
Because the first and last values cannot be at the centre of a complete group, there are fewer moving averages than original data points — a four-point moving average of 12 values gives 9 results.
Key points
- A moving average smooths a time series.
- The number of points matches the cycle length.
- Quarterly data uses a four-point moving average.
- Each is the mean of consecutive values.
- The group moves forward one position each time.
- There are fewer averages than data points.
Worked examples
Example 1
Work out the four-point moving average of 14, 18, 22 and 26. [2 marks]
Working
Example 2
Explain why a four-point moving average is used for quarterly data. [2 marks]
Working
Example 3
A time series has 10 values. Work out how many four-point moving averages can be calculated. [2 marks]
Working
Common mistakes
Using the wrong number of points.
It must match the cycle length in the data.
Expecting as many averages as data points.
There are always fewer, since complete groups are needed.
Plotting at the start of the group.
Plot at the centre of the group.
Forgetting to move the group by only one position.
Groups overlap; they do not partition the data.
Exam tips
- Match the number of points to the cycle length.
- Move the group forward one value at a time.
- Plot each average at the centre of its group.
- Remember this is a Higher-only topic.
Key terms
- Moving average
- The mean of consecutive values in a time series.
- Cycle
- The interval over which a seasonal pattern repeats.
- Smoothing
- Removing short-term variation to reveal the trend.
- Four-point moving average
- The average used for quarterly data.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.