What is an index number?
An index number measures how a quantity has changed relative to a chosen base value, written as a percentage. The base period always has an index of 100. A price index above 100 shows an increase; below 100 shows a decrease.
Key formula
Price index: I = (Q₁ / Q₀) × 100, where Q₀ is the base-time value and Q₁ is the current value. Rearranged: Q₁ = Q₀ × I / 100.
Reading the index
If the index of a good in 2024 based on 2020 is 125, its price rose by 25% over that period. An index of 90 would mean the price fell by 10%.
Worked example
The price of rice was RM4.00 in 2020 (base year) and RM5.00 in 2024. Find the price index for 2024 based on 2020. I = (Q₁/Q₀) × 100 = (5.00/4.00) × 100 = 1.25 × 100 = 125. The price increased by 25%. If instead the 2024 price were RM3.60, the index would be (3.60/4.00) × 100 = 90, a 10% fall.
Comparing over several years
Index numbers make comparisons easy because the base is fixed at 100. To find a later price when the index is known, rearrange to Q₁ = Q₀ × I/100. To chain from one base to another, multiply the successive index ratios: if the index in 2022 (base 2020) is 110 and in 2024 (base 2022) is 120, the 2024 index based on 2020 is (110 × 120)/100 = 132. Always state clearly which year is the base, since the same price data give different index values for different bases.
Remember
- Base value always has index 100.
- Index > 100 means increase; < 100 means decrease.
- Percentage change = index − 100.