Simple index numbers
- An index number shows how a value has changed compared with a base value, which has index 100.
- Index number = value ÷ base value × 100. If a price was £40 in the base year and is £46 now, the index is 46 ÷ 40 × 100 = 115.
- An index of 115 means a 15% increase since the base year; an index of 90 means a 10% decrease.
Chain base and weighted index numbers
- A chain base index compares each year with the year before. A chain base index of 105 means a 5% rise on the previous year.
- A weighted index number combines several items, giving each a weight for its importance. Weighted index = Σ(index × weight) ÷ Σweights. Indexes of 110 (weight 3) and 120 (weight 1) give (330 + 120) ÷ 4 = 112.5.
- The Consumer Prices Index (CPI) is a weighted index measuring inflation, using a basket of goods.
Rates
- A crude rate compares an event with the population size, usually per 1,000. Crude birth rate = births ÷ population × 1,000. With 600 births in a population of 50,000, the rate is 12 per 1,000.
- Crude rates can mislead when areas have different age structures: a seaside town with many older people has a higher crude death rate.
- A standardised rate adjusts for age using a standard population. Multiply each age group's rate by the proportion of the standard population in that group, then add. For example, 0.8 × 2 + 0.2 × 30 = 7.6 per 1,000.
Key terms
- Index number
- A value compared with a base value set at 100.
- Base year
- The year used for comparison, with index 100.
- Chain base index
- An index comparing each period with the one before.
- Weighted index number
- An index combining items according to their importance.
- Crude rate
- The number of events per 1,000 of the population.
- Standardised rate
- A rate adjusted for the age structure of the population.