Index Numbers
Simple and weighted index numbers, chain base index, RPI, CPI
Simple Index Numbers
An index number measures the change in a quantity relative to a base value. It is expressed as a number where the base period = 100.
Index Number = (Current value ÷ Base value) × 100
The price of a product was £40 in 2020 (base year) and £52 in 2024. Calculate the index number for 2024.
The reference period against which all other values are compared. The index number for the base period is always 100.
Weighted Index Numbers
A weighted index number takes into account the relative importance (weight) of each item.
Weighted Index = Σ(Index × Weight) ÷ Σ(Weight)
Food index = 120 (weight 4), Transport index = 110 (weight 2), Housing index = 130 (weight 6). Calculate the weighted index.
Chain Base Index
A chain base index compares each value to the previous period rather than to a fixed base year.
Chain Base Index = (Current value ÷ Previous value) × 100
Fixed base: all values compared to one base year. Useful for long-term comparisons. Chain base: each value compared to the previous year. Better for detecting year-on-year changes but harder to compare across many years.
RPI and CPI
A measure of inflation that tracks the average change in prices of a basket of goods and services, including housing costs (mortgage interest payments).
The UK government's preferred measure of inflation. Similar to RPI but excludes housing costs and uses a different averaging method.
RPI is generally higher than CPI because it includes housing costs. RPI is used for index-linking pensions and some benefits. CPI is used for the Bank of England's inflation target (2%).