Index Number — Definition, Formula & Examples
An index number is a statistical value that expresses a quantity (such as a price or production level) as a percentage of a base-period value. It makes it easy to see how much something has changed relative to a starting point.
An index number is a dimensionless ratio, typically multiplied by 100, that compares the value of a variable in a given period to its value in a designated base period, thereby standardizing the measurement of relative change across time or categories.
Key Formula
Where:
- = Index number for the given period
- = Value of the variable in the current period
- = Value of the variable in the base period
How It Works
You pick a base period and set its index value to 100. Then for every other period, you divide the current value by the base-period value and multiply by 100. A result above 100 means an increase relative to the base, and below 100 means a decrease. Index numbers let you compare trends even when the original units or scales differ.
Worked Example
Problem: A loaf of bread cost $2.00 in 2010 (base year) and $2.50 in 2023. Calculate the price index for 2023.
Identify values: The base-period value is $2.00 and the current-period value is $2.50.
Apply the formula: Divide the current value by the base value and multiply by 100.
Answer: The price index for 2023 is 125, meaning the price increased by 25% relative to 2010.
Why It Matters
Index numbers are the foundation of real-world indicators like the Consumer Price Index (CPI) and stock market indices. In economics and business courses, you will use them to track inflation, compare living costs, and analyze market trends over time.
Common Mistakes
Mistake: Confusing the index number with a percentage change.
Correction: An index of 125 does not mean a 125% increase. It means the value is 125% of the base, which is a 25% increase. Subtract 100 from the index to find the percentage change.