The Problem with "Average"
When someone says "the average salary in this field is $80,000," which average do they mean? The word "average" is used loosely in everyday language, but in statistics it can refer to three very different calculations — the mean, the median, and the mode. Knowing the difference isn't just academic trivia; it determines whether the number you're hearing actually represents what's being claimed.
The Three Types of Average
Mean (Arithmetic Average)
The mean is calculated by adding all values together and dividing by the count. It's what most people picture when they hear "average."
Formula: Mean = Sum of all values ÷ Number of values
Example: Salaries of $40,000, $50,000, $55,000, $60,000, and $200,000.
Mean = ($40,000 + $50,000 + $55,000 + $60,000 + $200,000) ÷ 5 = $81,000
Does that feel representative? Most people in this group earn far less than $81,000. That $200,000 outlier pulled the mean up dramatically.
Median (Middle Value)
The median is the middle value when all numbers are arranged in order. If there's an even number of values, it's the average of the two middle numbers.
Using the same salaries: $40,000, $50,000, $55,000, $60,000, $200,000
Median = $55,000
This is much more representative of what a typical person in this group earns. The median is resistant to outliers — extreme values don't move it much.
Mode (Most Frequent Value)
The mode is the value that appears most often in a dataset. It's most useful for categorical data or when you want to know the most common outcome.
Example: In a survey of shoe sizes — 7, 8, 8, 9, 8, 10, 9 — the mode is 8. A shoe retailer cares most about the mode when deciding stock quantities.
When to Use Each Measure
| Situation | Best Measure | Why |
|---|---|---|
| Incomes, house prices | Median | Outliers skew the mean significantly |
| Test scores (symmetric distribution) | Mean | Less skew; mean reflects center well |
| Most popular product, category | Mode | Frequency matters more than magnitude |
| Comparing salary offers | Median | Gives a realistic "typical" salary |
How Averages Are Used to Mislead
Choosing the "right" average is partly about context — but it's also sometimes a deliberate choice to tell a flattering story. A company might advertise its "average customer saves $500 per year" using a mean inflated by a handful of extreme savers, while most customers save far less. Governments sometimes prefer to report mean income growth because a rising stock market lifts wealthy people's incomes disproportionately, making the mean look rosier than the median.
Rule of thumb: When data involves incomes, prices, or anything influenced by wealth, look for the median. If you're only given a mean, ask why.
Skewness: Which Way Does the Data Lean?
In a perfectly symmetric dataset, the mean and median are the same. But most real-world data is skewed:
- Right-skewed (positive skew): A long tail to the right. Mean > Median. Common with income data.
- Left-skewed (negative skew): A long tail to the left. Mean < Median. Less common, but occurs in things like age at retirement.
Takeaways
- The mean is easily distorted by outliers — always ask if extreme values are present.
- The median is your best friend for understanding "typical" in skewed datasets.
- The mode tells you the most common value — useful for practical, categorical decisions.
- When you see "average," ask which average — and why that one was chosen.