Simple index numbers, the base year, the Retail Price Index and Consumer Price Index, and chain base and weighted index numbers.

What this dot point is asking

AQA wants you to calculate and interpret simple index numbers relative to a base year, understand the Retail Price Index and Consumer Price Index, and work with chain base and weighted index numbers. Index numbers connect to time series (tracking change over time) and to the weighted mean from the summarising-data module.

Simple index numbers and the base year

Setting the base year to $100$ makes change easy to read: the index minus $100$ is the percentage change since the base year. An index of $120$ is a $20\%$ rise, $95$ is a $5\%$ fall, and exactly $100$ means no change. Because the base is fixed, every later year is measured against the same starting point, which is ideal for showing the total change over a long period.

The Retail Price Index and Consumer Price Index

The "basket" is a weighted selection of typical purchases, updated periodically so it reflects what households actually buy. Because some items (food, fuel, housing) take a larger share of spending, they are given more weight, which is why the RPI is a weighted index rather than a simple average of individual price indices.

Chain base index numbers

A chain base index compares each year with the previous year rather than a fixed base, so it shows year-on-year change. An index of $105$ on a chain base means a $5\%$ rise on the year before, not on a fixed base year. Chain base indices are useful for spotting the rate of change from one year to the next, whereas a fixed base shows the cumulative change since the start.

Weighted index numbers

A weighted index is a weighted mean of the individual indices, so a large price rise on a low-weight item moves the overall index less than a small rise on a high-weight item. This matches reality: a doubling in the price of a rarely bought luxury barely affects a typical household, while a modest rise in food prices hits everyone.

Index numbers connect to several other topics. They are the natural way to track a price or quantity over time, so they pair with time series graphs and trend analysis. The weighted index is just the weighted mean from the summarising-data module applied to indices, so the same $\frac{\sum wx}{\sum w}$ formula reappears. And reading "index minus $100$ as a percentage change" is the everyday use of inflation figures reported in the news, which is exactly why exam questions are framed around fuel, food and housing costs. Being fluent with the simple index, the base year and the weighted index covers almost every question AQA sets on this topic.