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Time Series Graphs

FoundationHigherAQAEdexcel

Understand Time Series Graphs for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. A time series graph plots data collected at regular time intervals to reveal trends.

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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.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A time series graph plots data collected at regular intervals over time, with time always on the horizontal axis.

Three features may be present. The trend is the general long-term direction, rising, falling or flat. Seasonal variation is a pattern that repeats at regular intervals, such as higher sales every December. Random variation is the irregular fluctuation that remains once trend and seasonality are accounted for.

Separating these is what makes time series analysis useful. A single high value may reflect the trend, the season, or simply chance, and interpreting it correctly requires identifying which. Moving averages are used to smooth out seasonal and random variation so the underlying trend becomes visible.

Revision notes

The three components

Trend: the general long-term direction of the data.

Seasonal variation: a pattern repeating at regular intervals, such as quarterly or annually. Random variation: irregular fluctuation remaining after trend and seasonality are removed.

Reading a time series

Time always goes on the horizontal axis, with the measured variable on the vertical.

Points are plotted at each time period and joined with straight lines. Look for the overall direction first, then any repeating pattern.

Why separate the components

A single high value may reflect the trend, the season, or chance.

Interpreting it correctly requires identifying which. Moving averages smooth out seasonal and random variation so the underlying trend becomes visible.

Key points

  • Time series data is collected at regular intervals.
  • Time goes on the horizontal axis.
  • The trend is the long-term direction.
  • Seasonal variation repeats at regular intervals.
  • Random variation is irregular fluctuation.
  • Moving averages reveal the trend.

Worked examples

Example 1

Sales are consistently highest every December. State which component of a time series this represents. [1 mark]

Working

Seasonal variation, because the pattern repeats at the same point each yearidentify the component

Example 2

Explain what is meant by the trend in a time series. [2 marks]

Working

The trend is the general long-term direction of the datadefine the term
showing whether values are rising, falling or staying roughly level over time, ignoring short-term fluctuationsexplain what it shows

Example 3

Explain why moving averages are used with time series data. [2 marks]

Working

They smooth out seasonal and random variation in the datastate what they do
so the underlying trend becomes visible and can be identified more clearlyexplain the purpose

Common mistakes

  • Confusing trend with seasonal variation.

    The trend is long-term direction; seasonality repeats at regular intervals.

  • Putting time on the vertical axis.

    Time always goes on the horizontal axis.

  • Treating every fluctuation as meaningful.

    Some variation is random and should not be over-interpreted.

  • Describing the trend from two points only.

    The trend is the long-term direction across the whole series.

Exam tips

  • Identify the trend before looking at individual points.
  • Look for repeating patterns to spot seasonality.
  • Put time on the horizontal axis.
  • Link moving averages to revealing the trend.

Key terms

Time series
Data collected at regular intervals over time.
Trend
The general long-term direction of the data.
Seasonal variation
A pattern repeating at regular intervals.
Random variation
Irregular fluctuation with no pattern.

Related topics

Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.