Time series and index numbers - CCEA GCSE Statistics guide to moving averages, trend lines, seasonal variation and index numbers

Analysing data over time is a major part of Unit 2. This CCEA GCSE Statistics guide covers time series, moving averages and trend lines, and the index numbers used to measure change in prices and quantities.

Time series and trends

A time series plots a variable against time, with the points joined in order. It usually combines a trend, the general long-term direction, with seasonal variation, a pattern that repeats over a fixed period such as summer or winter. The raw graph zig-zags because the seasonal pattern hides the trend, so we smooth it to see the underlying movement.

Moving averages and the trend line

A moving average smooths the data by averaging a fixed number of consecutive values and moving along by one each time. The number of points must match the cycle length: four points for quarterly data, seven for daily data over a week, twelve for monthly data over a year. Plotting the moving averages and drawing a straight trend line through them shows the trend clearly. Each moving average is plotted at the centre of the values it averages. Extending the trend line predicts a future value, but only as an estimate, and a full seasonal prediction adds back how far that season usually sits above or below the trend.

Simple index numbers

An index number measures how a value has changed relative to a base year set at 100. It is the current value divided by the base value, times 100, so an index of 125 means a 25 percent rise and an index of 95 means a 5 percent fall. The index minus 100 gives the percentage change since the base year, and the same method works for prices or quantities.

The RPI, CPI and weighted index

The Retail Prices Index and Consumer Prices Index measure inflation by tracking the cost of a fixed basket of typical goods relative to a base year. They are weighted indices because some items make up a larger share of spending. A weighted index multiplies each item's index by a weight reflecting its importance, adds these, then divides by the total weight, so the result reflects real spending patterns rather than a simple average. A chain base compares each year with the previous one, showing the year-on-year rate of change.

How CCEA examines this topic

CCEA rewards calculating moving averages with the correct number of points, reading the trend, simple index-number calculations and their interpretation as a percentage change, weighted index numbers, and understanding the RPI and CPI as inflation measures. These topics run through the Unit 2 case study on real economic data over time. Use the dot points for specification-level detail and worked CCEA-style questions, then test yourself with the quiz.