## What is an aggregate function?

An aggregate function is a mathematical calculation that involves a range of values that results in a single value that expresses the importance of the accumulated data from which it is derived. Aggregate functions are often used to derive descriptive statistics.

Aggregate functions are often used in databases, spreadsheets, and statistical software packages that are now common in the workplace. Aggregate functions are widely used in economics and finance to provide key numbers that represent economic health or market performance.

Key takeaways

- Aggregate functions return a single number to represent a larger data set. The numbers that are used can themselves be products of aggregate functions.
- Many descriptive statistics are the result of aggregate functions.
- Economists use the results of data aggregation to chart changes over time and project future trends.
- Models created from aggregated data can be used to influence political and business decisions.

## Understanding the aggregate function

The aggregate function simply refers to the calculations performed on a data set to obtain a single number that accurately represents the underlying data. The use of computers has improved the way these calculations are performed, allowing aggregate functions to produce results very quickly and even adjust the weights based on how confident the user is in the data. Thanks to computers, aggregate functions can handle increasingly large and complex data sets.

Some common aggregate functions include:

- Average (also called arithmetic mean)
- Tell
- Maximum
- Minimum
- Distance
- NaNmean (the mean that ignores NaN values, also known as “nil” or “null”)
- Median
- Mode
- Sum

## Aggregate functions in economic models

The math for aggregate functions can be quite simple, like finding the average US gross domestic product (GDP) growth over the past 10 years. Given a list of GDP figures, which itself is a product of an aggregate function in a data set, you would find the difference from year to year and then add the differences and divide by 10. The math is doable with pencil and On paper, but imagine trying to do that calculation for a data set that contains GDP figures for every country in the world. In this case, an Excel sheet greatly reduces processing time and a programmatic solution like modeling software is even better. This type of processing power has greatly helped economists perform aggregate function sets on massive data sets.

Econometrics and other fields within the discipline use aggregate functions on a daily basis and sometimes recognize it in the name of the resulting figure. Aggregate supply and demand is a visual representation of the results of two aggregate functions, one performed on a production data set and the other on an expense data set. The aggregate demand curve is produced from a similar spending data set and shows the aggregated number of subsets drawn over a period to produce a curve showing changes over the time series. This type of visualization or modeling helps to show the current state of the economy and can be used to inform real-world business decisions and policies.

## Aggregate functions in business

Obviously, there are many added functions in business: added costs, added revenue, added hours, and so on. That said, one of the most interesting ways the aggregation function is used in finance is by modeling aggregate risk.

Financial institutions, in particular, are required to provide easily understandable summaries of their exposure. This means summarizing your particular counterparty risks, as well as the added value at risk. The calculations used to arrive at these numbers must accurately reflect the risks that are themselves probabilities based on data sets.

With a high level of complexity, a sunny guess in the wrong place can undermine the entire model. This exact problem played a role in the consequences of the Lehman Brothers collapse.