Skip to main content
EnglandStatisticsSyllabus dot point

How do moving averages reveal the trend in seasonal data and support predictions?

Time series graphs; identifying trends by inspection and by calculating moving averages; plotting a trend line; interpreting seasonal and cyclic variation; using trends and seasonal effects to predict.

A focused answer to Edexcel GCSE Statistics on time series, covering time series graphs, identifying trends by inspection and by moving averages, plotting a trend line, interpreting seasonal and cyclic variation, and using the trend and seasonal effect to make predictions.

Generated by Claude Opus 4.810 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

Have a quick question? Jump to the Q&A page

Jump to a section
  1. What this dot point is asking
  2. Time series graphs
  3. Moving averages
  4. The trend line
  5. Seasonal and cyclic variation
  6. Predicting with trend and seasonal effect

What this dot point is asking

Edexcel codes 2f.01 and 2f.02 require you to identify trends in a time series by inspection and by calculating moving averages, to plot a trend line, to interpret seasonal and cyclic variation in context, and (Higher tier) to use the trend and average seasonal effect to make predictions. Moving average calculations and "predict the next value" questions appear regularly, and the seasonal effect ties the topic together.

Time series graphs

Raw time series data often zig-zags because of seasonal variation (for example sales peaking each summer), which can hide the underlying long-term movement. Smoothing the data lets you see the trend clearly.

Moving averages

A moving average smooths the data by repeatedly averaging a fixed number of consecutive values. For quarterly data you use a 44-point moving average (one full year), so the seasonal pattern averages out.

Each moving average is plotted at the middle of the values it covers. The number of points chosen should match the length of the seasonal cycle (4 for quarters, 7 for days of the week), so that one whole cycle is averaged each time.

The trend line

Plotting the moving averages and drawing a line through them gives the trend line, which shows the long-term direction once the seasonal noise is removed. The gradient of the trend line is interpreted in context: a positive gradient means the quantity is rising over time, a negative gradient means it is falling. Edexcel expects you to describe the trend ("sales are increasing year on year") rather than just draw the line.

Seasonal and cyclic variation

Seasonal variation is the regular short-term pattern that repeats each cycle (higher sales in Q4, lower in Q1). Cyclic variation is a longer, less regular wave (for example an economic cycle). The seasonal effect for a given season is how far that season typically lies above or below the trend:

seasonal effect=actual value−trend value.\text{seasonal effect} = \text{actual value} - \text{trend value}.

Averaging the seasonal effect for a season across several cycles gives the mean seasonal effect, used for prediction.

Predicting with trend and seasonal effect

To predict a future value (Higher tier), extend the trend line to read off the future trend value, then add the mean seasonal effect for that season:

prediction=trend value+mean seasonal effect.\text{prediction} = \text{trend value} + \text{mean seasonal effect}.

This is more reliable than reading the raw graph, but it still assumes the trend and seasonal pattern continue, so predictions far ahead (extrapolation) are risky.

Exam-style practice questions

Practice questions written in the style of Pearson Edexcel exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Edexcel 1ST0 20204 marksA shop records quarterly sales (in GBP thousands): Q1 2020, Q2 3232, Q3 2828, Q4 4444, then Q1 2424. Calculate the first three 44-point moving averages.
Show worked answer →

A 44-point moving average averages four consecutive quarters and moves along one at a time.

First: 20+32+28+444=1244=31\frac{20 + 32 + 28 + 44}{4} = \frac{124}{4} = 31.

Second: 32+28+44+244=1284=32\frac{32 + 28 + 44 + 24}{4} = \frac{128}{4} = 32.

For a third value a sixth quarter would be needed; with the data given only two 44-point moving averages can be found, so state that and give 3131 and 3232.

Markers reward the method (mean of four consecutive values, moving along by one) and the correct values 3131 and 3232; recognising that the data only supports two moving averages is also creditworthy.

Edexcel 1ST0 20224 marksA time series of quarterly ice cream sales shows a rising trend line. In a given quarter the trend value is 5050 (GBP thousand) and the mean seasonal effect for that quarter (summer) is +15+15. (a) Use these to predict the sales for that quarter. (b) State one reason why the prediction might be unreliable.
Show worked answer →

(a) Prediction == trend value ++ seasonal effect =50+15=65= 50 + 15 = 65 (GBP thousand).

(b) Any valid reason, for example: the prediction assumes the trend and the seasonal pattern continue unchanged, but unusual weather, economic change or extrapolating too far ahead could make it wrong.

Markers reward adding the trend value and seasonal effect to get 6565, and one valid reason about the assumptions or the danger of extrapolation.

Related dot points

Sources & how we know this