## What is Aggregate Function?

An aggregate function is a mathematical computation involving a set of values that results in a single value expressing the significance of the data it is computed from. Aggregate functions are often used in databases, spreadsheets and many other data manipulation software packages now common in the workplace. In the context of finance, aggregate functions are used extensively in economics and finance to provide key numbers that represent the economic health or stock and sector performance.

### Key Takeaways

- Aggregate functions deliver a single number to represent a data set. The numbers being used may themselves be products of aggregate functions.
- Economists use the outputs of data aggregation to plot changes over time and project future trends.
- The models created out of aggregated data can be used to influence policy and business decisions.

## Understanding Aggregate Function

Aggregate function simply refers to the calculations performed on a data set to get a single number that accurately represents the underlying data. The use of computers has improved how these calculations are performed, allowing aggregate functions to produce results very quickly and even adjust weightings based on the confidence the user has in the data. Thanks to computers, aggregate functions can handle ever larger and more complex data sets.

Common aggregate functions include:

- Average (also called arithmetic mean)
- Count
- Maximum
- nanmean (mean ignoring NaN values, also known as "nil" or "null")
- Median
- Minimum
- Mode
- Sum

## Aggregate Functions in Economic Modelling

The mathematics for aggregate functions can be quite simple, such as finding the average gross domestic product (GDP) growth for the U.S. over the last 10 years. Given a list of GDP figures, which itself is a product of an aggregate function on a data set, you would find the difference year to year and then sum up the differences and divide by 10. The math is doable with pencil and paper, but imagine trying to do that calculation for a data set containing GDP figures for every country in the world. In this case, an excel sheet greatly reduces the processing time and a programmatic solution like modelling software is even better. This type of processing power has greatly helped economists in performing suites of aggregate functions on massive data sets.

Econometrics and other fields within the discipline use aggregate functions daily, and they sometimes recognize that in the name of the resulting figure. Aggregate supply and demand is a visual representation of the results of two aggregate function, one performed on a production data set and another on a spending data set. The aggregate demand curve is produced out of a similar spending data set and shows the aggregate number of the subsets plotted over time to produce a curve showing changes over the time series. This type of visualization or modelling helps show the current state of the economy and can be used to inform real world policy and business decisions.

## Aggregate Functions in Business

Obviously there are many aggregate function in business - aggregate costs, aggregate income, aggregate hours and so on. That said, one of the more interesting ways the aggregation function is used in finance is in modelling aggregate risk. Financial institutions, in particular, are required to provide easily understood summaries of their exposure. This means summarizing their particular counterparty risks as well as the aggregate value at risk. The calculations used to come up with these numbers must accurately reflect risks which themselves are probabilities based on data sets. With high level of complexity, a sunny assumption in the wrong place can undermine the whole model. This exact problem played a role in the fallout around the Lehman Brothers collapse.