Simple index numbers; chain base index numbers; weighted index numbers; the retail price index, consumer price index and gross domestic product; calculating and interpreting index numbers in context.

What this dot point is asking

Edexcel code 2d.01 requires you to use index numbers in context, including the retail price index (RPI), consumer price index (CPI) and gross domestic product (GDP). You must calculate and interpret simple index numbers and chain base index numbers, and (Higher tier) weighted index numbers. Index numbers are how the topic connects statistics to inflation and the economy, so interpretation in context is essential.

Simple index numbers

Because the base is $100$, the index minus $100$ is directly the percentage change: an index of $112$ is a $12\%$ increase, and $94$ is a $6\%$ decrease. This makes index numbers a quick way to compare change across different items measured in different units.

Chain base index numbers

A chain base index compares each value with the previous period rather than a single fixed base year. Each year's chain index is $\frac{\text{this year}}{\text{last year}} \times 100$, so it measures the year-on-year change. Chain base indices are useful for tracking how the rate of change varies over time (for example whether inflation is speeding up or slowing down), where a fixed base year would obscure the short-term movements.

Weighted index numbers

In real life some items matter more than others, so a single average of indices would mislead. A weighted index number (Higher tier) combines individual indices using weights that reflect their importance (for example how much a household spends on each item).

This is a weighted mean of the indices. The RPI and CPI are real-world weighted indices: they track a "basket" of goods and services, weighting each by how much a typical household spends on it.

RPI, CPI and GDP

• Retail price index (RPI) and consumer price index (CPI) measure the average change in the price of a basket of household goods and services over time, so they measure the cost of living and inflation. The CPI excludes some housing costs that the RPI includes, so the two can differ.
• Gross domestic product (GDP) measures the total value of goods and services produced by an economy, often expressed as an index to show growth over time.

Edexcel expects you to interpret these in context, for example "a CPI of $108$ means prices are $8\%$ higher than in the base year, so the cost of living has risen".

Comparing index numbers over several years

When a table gives index numbers for several years (all with the same base year), you can compare any two years directly. Because each index is a percentage of the same base, the difference between two indices is the change relative to the base, but the percentage change between the two years themselves must be calculated from the indices: $\frac{\text{later index} - \text{earlier index}}{\text{earlier index}} \times 100$. For example, going from an index of $120$ to $150$ is a rise of $\frac{150 - 120}{120} \times 100 = 25\%$ over that period, even though both are measured against the original base. Mixing up "change since the base year" with "change between two later years" is a frequent slip.

Why index numbers are useful

Index numbers let you track and compare change across items that are measured in different units or at very different magnitudes. By rescaling everything so the base is $100$, a 5 pence rise in a cheap item and a GBP $50$ rise in an expensive one can be compared on the same footing through their indices. This is why economists use them for prices, wages, output and many other quantities, and why a single weighted index can summarise the overall change across a whole basket of goods.