# How to Calculate Index Numbers

Index numbers provide a simple, easy-to-digest way of presenting various types of data and analyzing changes over time. Create an index with a time series of information, using simple division and multiplication to calculate the index numbers and convert various types of data into a uniform format. Use the output for various analyses, including measuring your subject's growth and comparing and contrasting with other sets of data.

## Use an Index for Simplification

An index measures changes against a base value in a simplified fashion. Some well-known examples include the Consumer Price Index (CPI) and Standard & Poor’s 500 stock index, better known as the S&P 500. Working with a group of large numbers is sometimes inefficient and confusing, and an index allows you to use a simplified value to easily compare and track against other data points over time.

For example, the U.S. as a whole provides about 140 million jobs. Using an index to simplify the numbers, you can easily compare its percentage job growth over time to that of the state of Texas, even though Texas has only about 20 million jobs. Converting the data to index values makes it easier to see the percentage change each year when comparing the two sets of data side by side, even though the magnitude of jobs for the whole U.S. dwarfs the number of jobs in Texas.

An index starts with a base value, typically set at 100, regardless of whether the index measures data units in dollars, euros, or headcount, for example. Each subsequent value in the index is then normalized to this base value. When looking at the percent change between different calculated index values, you will find that it’s exactly the same as the un-normalized or non-indexed data percent change. Using an index to measure changes in data allows you to calculate the percentage change between the points in the index without the need to know the actual data numbers. The index points become normalized when dividing each number by its base value, meaning that the values on different scales become converted into a common scale for ease of comparison.

## Calculate Index Values

The first step in constructing an index involves setting the base value. For a time series of annual company sales, for example, say the first year, sales were $150,000. This base-year amount is set to equate to the starting index value of 100. Each added value becomes normalized against the base value. To calculate the value of the next data point in this indexed time series, let’s say the second year of annual sales equates to $225,000. You would divide the new data point ($225,000) by the original one ($150,000), multiplying the result by 100 as follows to get a year 2 index value of 167.

**(Year 2 sales of $250,000 / Base year sales of $150,000) * 100 = 167**

Each new year of data is subsequently normalized against the base year of $150,000 in the same fashion. If years 3, 4 and 5 had sales of $325,000, $385,000 and $415,000, the corresponding calculated index values would be 217, 257 and 277, respectively.

## Interpretation Issues

When using an index to track changes over time, you may find that the data changes and becomes less comparable to the original, or base data. For example, when tracking unit sales of a product over time, the price may experience a permanent increase. Although unit sales of the product haven’t actually grown, the index shows growth because of the product’s new, higher price. In terms of an index measuring changes over time using a market basket of goods and services, such as the CPI, some goods or products may increase in price, change in quality or other features that make them no longer comparable against the original base value of the index or its earlier data points. Compensating for this issue, although not a perfect solution, would require updating the base basket of goods and earlier data points periodically to reflect and compensate for these types of changes.