The Recruiter Who Used the Wrong Average
A recruiter once told me the "average" salary at their company was $145,000. I asked for the median. $89,000. Guess which number they put in the job listing.
The CEO made $1.2 million. Two VPs made $400k each. That pulled the mean up by $56,000 over the median — a number that better represents what most employees actually earn. Same dataset, two "averages," two completely different stories.
This isn't a math trick. It's the most common way data gets used to mislead, and it happens in salary reports, real estate listings, and government statistics every single day.
Mean: Add Everything, Divide by Count
Five software engineers at a startup earn: $75k, $82k, $89k, $95k, and $380k. That last one is the CTO who also codes.
$144,200. Not a single person on that team actually earns that amount. The CTO's salary yanked the average up by $55,000 over what the typical engineer makes. The mean is honest — it's mathematically correct — but it's misleading when outliers exist.
This is exactly why the Bureau of Labor Statistics reports median household income, not mean. They know the billionaires would wreck the number.
Median: The Middle Kid Gets It Right
Line up the same five salaries in order: $75k, $82k, $89k, $95k, $380k. The middle value is $89k. That's the median.
The CTO's $380k doesn't budge it. Replace $380k with $3.8 million and the median is still $89k. That's the superpower of the median: it's immune to extremes.
Same Data, Different "Average"
One outlier pulls the mean $55k above the median
When someone says "average home price in this neighborhood is $850,000," ask: mean or median? If one mansion sold for $4 million last month, the mean could be wildly misleading. Real estate agents know this. They pick whichever number makes the listing look better.
Mode: The One Nobody Remembers (Until They Need It)
Mode is the most frequently occurring value. In the salary dataset above, there is no mode — every value appears once. Mode is useless for continuous data like salaries or temperatures.
Where mode shines: categorical data. What's the most popular shoe size at a store? The most common response on a survey? The most frequent error code in a server log? Mean and median can't answer these questions. Mode can.
A dataset can have no mode, one mode, or multiple modes (bimodal, multimodal). If your class test scores cluster around both 65 and 90, that bimodal distribution tells you something important — the class has two distinct groups, and the mean of 77 represents neither of them.
The Decision Framework: Which One Do I Use?
Use Mean When...
Data is roughly symmetric with no extreme outliers. Test scores in a normal class, daily temperatures over a month, manufacturing measurements. The mean uses every data point, which is its strength and weakness.
Use Median When...
Data is skewed or has outliers. Income, home prices, hospital wait times, wealth distribution. Anything where a few extreme values would distort the "typical" picture.
Your GPA is a weighted mean — and it hides the same kind of detail. A 3.5 GPA could mean all B+'s, or it could mean half A's and half C's. The average tells you the center but not the shape.
The p-value faces a similar problem — a single number that gets treated as the whole story when it's really just one piece of the puzzle.
Frequently Asked Questions
What's the difference between mean and median?
Mean adds all values and divides by count — it's sensitive to outliers. Median is the middle value when data is sorted — it's resistant to outliers. For symmetric data they're nearly identical. For skewed data (income, home prices), median better represents the "typical" value.
When should I use mode instead of mean?
Use mode for categorical data where mean and median don't make sense — most popular product, most common survey response, most frequent error type. Mode is also useful for identifying clusters in bimodal distributions where the mean falls between two peaks and represents neither group.
Why do salary reports use median instead of mean?
Because executive compensation skews the mean upward dramatically. A company where most people earn $70-90k but the CEO earns $5M would show a mean salary far above what any typical employee earns. The median ignores the extremes and shows what the middle person actually makes.