How do index numbers measure change over time, and how are the RPI, CPI and a weighted index used and interpreted?
Calculate and interpret simple index numbers, understand the Retail Prices Index and Consumer Prices Index, find a weighted index number, and use a chain base to compare year-on-year change.
A CCEA GCSE Statistics answer on index numbers: simple price and quantity index numbers, the base year, the Retail Prices Index and Consumer Prices Index, weighted index numbers, and the chain base method.
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What this dot point is asking
An index number measures how a quantity, price or value has changed relative to a base year, which is set at 100. CCEA expects you to calculate and interpret simple index numbers, understand the Retail Prices Index (RPI) and Consumer Prices Index (CPI) as measures of inflation, calculate a weighted index number, and use a chain base to compare year-on-year change. The simple-index calculation and the weighted index are the key skills.
Simple index numbers
An index number expresses a value as a percentage of its base-year value.
So an index of 112 means a 12% rise since the base year, and an index of 95 means a 5% fall. The same idea works for prices (a price index) or quantities (a quantity index).
The RPI and CPI
The Retail Prices Index and the Consumer Prices Index are the government's main measures of inflation.
These indices are weighted, because some items (such as food or housing) make up a larger share of typical spending than others.
Weighted index numbers
A weighted index number allows for the fact that some items matter more than others.
The weights make the result reflect real spending patterns, which is why a national inflation figure is a weighted index, not a simple average of price changes.
The chain base
A chain base index compares each year with the previous year rather than with one fixed base year. Each year's chain-base index is the current value divided by the previous year's value, times 100, so it shows the year-on-year rate of change. A chain base of 104 one year and 102 the next means prices rose 4% then a further 2%, which is useful for tracking how the rate of change itself varies over time. A fixed-base index, by contrast, keeps comparing with the same base year, so it shows the total change since that year but hides how the year-on-year rate has slowed or accelerated. Choosing between them depends on whether you want the long-run change or the annual change.
Why this matters
Index numbers are how inflation, the cost of living, share prices and wages are reported and compared, so they are a genuinely important life skill, and they feature in the Unit 2 case study on real Northern Ireland economic data. The weighted index links straight back to the weighted mean, and the base-year idea underpins all comparisons over time. Reading an index correctly, as a percentage change from the base, is a frequent and reliable exam mark.
Exam-style practice questions
Practice questions written in the style of CCEA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
CCEA-style3 marksA loaf of bread cost 80p in the base year and costs £1.00 now. Calculate the price index for now, taking the base year as 100, and state what it means.Show worked answer →
Price index .
Two marks (method and value). It means the price has risen by since the base year, because the index of is above the base of . One mark for the interpretation. Index numbers always compare with the base year, which is set at .
CCEA-style4 marksThree items have price indices 110, 120 and 130, with weights 5, 3 and 2. Calculate the weighted index number.Show worked answer →
A weighted index multiplies each index by its weight, adds these, then divides by the total weight.
Weighted total .
Total weight . Weighted index .
Four marks (products, sum, total weight, division). The weights reflect how important each item is, so the most heavily weighted item (index 110) pulls the result down towards itself, giving 117 rather than a simple average of 120.
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Sources & how we know this
- CCEA GCSE Statistics (2017) specification (2260) — CCEA (2017)