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Index Number and Reference Value

Index Number and Reference Value

Author: Jonathan Osters

Identify index numbers from a reference value.

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Source: Milk photo taken by Joseph Gearin, CPI Index, Public Domain:

Video Transcription

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This tutorial is going to teach you about index numbers and reference values.

An index number is a way to measure a percent increase or decrease from one point to another. In time this is typically done with price changes. So we set an arbitrary starting point in time and assign that price an index number of 100. This starting price is called the reference value. Because we refer back to it every time the price changes.

For example, in 1983 a gallon of milk cost $2.24. We're going to assign a reference value of $2.24 an index value of 100. Essentially this means that it cost 100% of what it cost in 1983, pretty obvious statement. To calculate the index value for other points in time, like in 1988 when a gallon of milk costs $2.30, or 1993 when it cost $2.86, or 1998 when it costs $3.16, we take the current price, divide by the reference value of $2.24, and then convert that value to a percent.

So the index value in 1998, for instance, is $2.30 divided by the reference value of $2.24. That gives you 1.027 which as a percent is 102.7%. And index values are expressed without the percent symbol. As a result the index value in 1988 was 102.7.

We can complete the table with the remaining values. What this indicates is that by the time you got to 2003 a gallon of milk cost 142.4% as much as it did in 1983, A 42% increase over 1983.

The most prominent index number that you see in everyday life is called the consumer price index. It measures a percent increase or decrease in the price of goods and services. It's reference value is 1983, which is why I used it in the previous example. The US Bureau of Labor Statistics updates the CPI, the consumer price index, updates the CPI every month. What the CPI does it's a general measure of inflation.

Inflation means that the index is going up. It's a decline in purchasing power. What it means is that it costs more now to buy these goods and services than it did then. That means that the dollar is inflated. Meaning with the same amount of money coming in, with the same income, you have less purchasing power. It may cost you much more now to do what it costs $100 to do in 1983.

Here's a graph of the CPI over time. Notice the index value is 100 in 1983, between 1980 and 1990. Goods and services costing $100 in 1983 if you look at around 2007 would cost you around $200. The index value is 200 in 2007.

So to recap index numbers allow us to check changes, typically in prices, from one point in time to another. We begin with a reference value which is the price at some arbitrary point in time. And the index numbers are the percent increase or decrease from that reference value. If the price goes up the index number will be over 100. If the price goes down the index number will be under 100.

The most commonly referred to index would be the consumer price index. And that shows percent increase or decrease in the prices of many goods and services. So we talked about index numbers, and reference values, and put a practical spin on it with the consumer price index and talking about inflation. Good luck. And we'll see you next time.

Terms to Know
Consumer Price Index

An index published by the US Bureau of Labor Statistics that shows the change in the price of many different goods or services in the United States. It provides a measure of purchasing power.

Index Number

A way to measure the relative change in a value, usually the price of a good or service, over time. If the index number is over 100, that means the price has increased. If the price has decreased, then the index number will be less than 100.


A relative increase in the price of a good or service over time. A person will need to pay more to receive the same good or service than they did at a previous point in time.

Reference Value

An arbitrarily chosen starting value for an index. It is assigned an index number of 100.

Formulas to Know
Index Number

fraction numerator n e w space v a l u e over denominator r e f e r e n c e space v a l u e end fraction cross times 100