# What is an Index Number

Index numbers are a statistician's method of expressing the difference between two measurements by assigning one number as the "base", and then expressing the second number in terms of the first.

Example1: If the number of students in a school increased from 4000 in 2000 to 4200 in 2001, the population in 2001 was 105% of the population in 2000. Therefore taking 100 as base, the population index for the town was 105 in 2001.

Example 2: the numbers
 50 75 90 110 100

expressed as an index, with the first number as a base, would be

 100 150 180 220 200

Indexes can be used to express comparisons between prices, industries, population, etc. but the most common use is to express changes over a period of time. One point in time is designated the base periodâ€”it may be a year, month, or any other periodâ€”and given the value 100. If the index numbers for the measurement (price, quantity, value, etc.) at all other points in time indicate the percentage change from the base period. Then, if the price, quantity or value has increased by 25% since the base period, the index is 125; if it has fallen 9%, the index is 91. It is important to note that indexes reflect percentage differences relative to the base year and not absolute levels. If the price index for one item is 110 and for another is 105, it means the price of the first has increased twice as much as the price of the second. It does not mean that the first item is more expensive than the second.

People consume the services of thousands of commodities every year and most producers utilize and/or produce thousands of customized products and services. Index numbers are used to reduce and summarize this mind-boggling abundance of microeconomic information. Hence index numbers impose themselves on almost every empirical investigation in economics.

Normally, in economics, index numbers are time series data in a group of related variables. Nonetheless, index numbers may compare geographic areas at a point in time. A fine example is a country's purchasing power parity. The best-known index number is the consumer price index, which measures changes in retail prices paid by consumers. In addition, a cost-of-living index (COLI) is a price index number that measures relative cost of living over time.