Edexcel GCSE Statistics Time series and index numbers: moving averages, trends, RPI, CPI and crude rates

What this topic demands

This topic is about data over time and comparing values across time or place. Edexcel tests moving averages and trends, index numbers (including the real-world RPI, CPI and GDP), and rates of change such as crude birth and death rates. The headline calculations are the 4-point moving average with a prediction, the index number and weighted index, and the crude rate formula, all interpreted in context.

This guide covers the three dot-point pages on time series and index numbers, then sets out the exam patterns Edexcel repeats.

Time series and moving averages

Time series and moving averages covers time series graphs, identifying trends by inspection and by calculating moving averages, plotting a trend line, and interpreting seasonal and cyclic variation. A 4-point moving average smooths quarterly data; you plot it at the centre of its values. At Higher tier you predict with trend value plus mean seasonal effect, where seasonal effect $=$ actual value $-$ trend value.

Index numbers

Index numbers covers simple index numbers ($\frac{\text{current}}{\text{base}} \times 100$), chain base index numbers (each year against the previous), and weighted index numbers ($\frac{\sum (w \times \text{index})}{\sum w}$). The retail price index and consumer price index measure inflation, and GDP measures the size of an economy; all are interpreted in context.

Rates of change and crude rates

Rates of change and crude rates covers percentage change ($\frac{\text{change}}{\text{original}} \times 100$), crude birth and death rates (with the given formula, per $1000$ of population), and (at Higher) standardised rates that adjust for age structure. Rates let you compare populations of different sizes fairly, and predictions from rates assume the trend continues.

How this topic is examined

A typical Edexcel profile:

• Moving averages. Calculating them and drawing or interpreting the trend line.
• Prediction. Trend value plus mean seasonal effect, with comment on extrapolation.
• Index numbers. Simple and weighted index calculations and interpretation.
• Rates. Crude rates with units, and comparing populations.

Check your knowledge

Attempt these under timed conditions, then check against the solutions.

1. What is the first 4-point moving average of $20, 32, 28, 44$? (1 mark)
2. A value was GBP $40$ and is now GBP $50$. Calculate the percentage change. (2 marks)
3. With base year $100$, a price index is now $130$. By what percentage has the price risen? (1 mark)
4. State the formula for the crude birth rate. (1 mark)
5. A town of $40000$ has $520$ births in a year. Calculate the crude birth rate. (2 marks)
6. To predict a value from a time series, what do you add to the trend value? (1 mark)
7. What do the RPI and CPI measure? (1 mark)
8. What does a weighted index account for that a simple average of indices does not? (1 mark)