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?
- 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.
What is it?
The mean is the sum of a set of values divided the total number of values in that set.
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.
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.
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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