The Average Salary Lies: Mean, Median and What Headlines Hide

"The average salary at our company is $18,500 a month!" It sounds generous until you notice that nobody you know earns anything close to it. Averages are the most quoted numbers in the news, and they quietly mislead more often than people realize.

A company of ten

Imagine ten employees with monthly pay of 8,500; 9,000; 9,500; 10,000; 10,500; 11,000; 11,500; 12,000; 13,000 and 90,000 dollars. Enter them into the descriptive statistics calculator and the mean comes out at 18,500. Yet nine of the ten earn less than that, and the typical employee earns about 10,750, the median.

The single 90,000 salary, perhaps the owner's, pulls the mean upward. Remove it and the mean of the other nine falls to about 10,556, nearly identical to the median. The median barely noticed the outlier, which is why statisticians prefer it for skewed data such as income, house prices and company size.

Try a quick experiment. Replace 90,000 with 13,500 and the mean drops to about 10,850 while the median stays at 10,750. Replace it with 900,000 and the mean jumps to nearly 100,000 while the median still does not move. Resistant statistics do not care how extreme the extreme is.

Reading the whole distribution

A single number can never describe a group. The five-number summary calculator reports the minimum, quartiles, median and maximum: here 8,500; 9,625; 10,750; 11,875; and 90,000. The enormous gap between the third quartile and the maximum reveals the skew immediately.

The standard deviation calculator adds another clue. The sample standard deviation is about 25,160, more than twice the median, while without the outlier it is only about 1,470. When the spread is huge relative to the typical value, a few extreme observations are probably doing the talking.

For larger datasets, a histogram is the clearest tool. The continuous frequency table and histogram calculator groups values into classes and shows a long right tail, the classic shape of income data. When the mean sits above the median, suspect right skew. Pair it with the quartiles from the summary and the whole shape of pay becomes visible.

Questions to ask about any "average"

Which average is it: mean, median or mode? Who is included: full-time staff only, or everyone? Is the figure before or after tax, and for what period? A national average can even rise while most people earn the same as last year, simply because top earners gained. Ask these questions before sharing or believing any pay headline.

Other ways to describe "typical"

The mode, the most frequent value, suits categories better than pay. In our company no salary repeats, so there is no mode, a reminder that each average answers a different question. Statisticians also use a trimmed mean, which discards a fixed share of the highest and lowest values before averaging, or the interquartile range, here 2,250, which ignores the extremes entirely.

Beware comparisons across years or groups, too. If a company hires many junior staff, its average pay falls even when every existing employee receives a raise, because the mix of people changed. This is a close cousin of Simpson's paradox.

Whenever you publish pay data, report the median and quartiles beside the mean, and say which one you mean. It costs one extra sentence and protects readers from the wrong conclusion.

The median is not always better, though. When budgeting total payroll, the mean is exactly what you need, because it scales with the sum.

Choosing a statistic means choosing the question you want answered.