## Averages: What Do They Really Mean? Part 1

The average (also called the mean) is the single most frequently used measure in analytics. But what happens when Bill Gates or a cluster of entry-level accountants enter the picture?

## Summary Points

- The mean is the most common measure in HR analytics
- The mean uses all of the data available so it can be a good representation of the measure you are interested in.
- Extreme values (such as Bill Gates’ salary) or large set of people on one end of the scale can produce misleading measures.

## The Basics

### What is it?

The mean is the sum of a set of values divided the total number of values in that set.

### Example

Let’s suppose that our manager, Susan, has three direct reports with the following salaries: $77,000, $53,000, and $50,000. To compute the mean (or average) we first simply sum the salaries ($77,000 + $53,000 + $50,000 = $180,000). Then we divide that total by three ($180,000/3), giving us an average salary of $60,000 for Susan’s direct reports.

### Squiggly Math Stuff (Optional)

Formally, the mean can be written as follows:

The symbol is read as “X bar” and represents the mean. The symbol Σ is called “sigma” and tells you to sum all of the values in our set of numbers *X* . This total is divided by *n, *which represents the count of the numbers in *X.*

__Why should I care?__

The mean is the most popular summary statistic for two reasons.

- The mean uses all of the data points available. As we will see in later tutorials, this means it is usually a good representation of the measure you are interested in.

- The mean is easy to calculate and easy to interpret. Moreover, it gives us a single number that allows us to easily compare data across different groups (for example, salaries for physicians v. actuaries)

## When Does the Mean Work Well?

The mean works really well when the values we are measuring are fairly balanced. For example, consider the mean salaries for a set of our accountants. Let’s suppose we have a few junior-level accountants earning, say, $65,000, many mid-level accountants earning roughly $100,000, and perhaps a few more senior accountants earning $135,000.

This is a fairly balanced group with some people earning a little less, some earning a little more, and a bunch of people right in the middle. There are no extremely high or extremely low values so a single salary one way or the other is not dramatically impacting our mean salary.

## When the Mean Doesn’t Work: Of Bill Gates And Entry-Level Accountants

- Means can be misleading or incredibly distorted in the presence of an extremely high or extremely low value (known as outliers).

For example, if I took the average salary of 1000 people with some college education who are over 50, I might expect to get a mean around $47,000.

But what if my sample also happens to include Bill Gates?

As our figure shows, suddenly my average salary for those over 50 with some college education balloons from $47,000 to just over $2 million. That’s a big difference…and an average that no longer reflects reality.

- Means can also be misleading when the sample of values are not balanced. For example, let’s suppose Company A has a pool of 20 accountants earning an average of $97,000 a year. But what if Company A now anticipates massive growth in its financial services area and hires 20 additional accountants fresh out of school?

As you can see, this huge influx of entry-level accountants earning entry-level accountant salaries (say, $65,000) would drive the average salary down substantially.

To outsiders, such a low average might signal that the company is cheap and severely underpays its employees; knowing the distributions and the history tells us otherwise.

## Additional Notes

These kinds of impacts tend not happen with naturally limited measures such as height or age; I am never going to find someone that is 873 feet tall or 1465 years old. Salary measures and other less constrained measures are another matter.

## What’s next?

In Part 2, we will cover how to know when your mean might be misleading and what to do about it.

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