Mean, Median & Mode โ The Complete Guide
Mean, median, and mode are the three "measures of central tendency" โ three different ways of answering the same question: where does this data set centre? They usually agree closely for symmetric, well-behaved data, but they can diverge sharply once outliers or skew enter the picture, which is exactly why it's worth calculating all three rather than defaulting to whichever one a spreadsheet function happens to return first.
The Three Measures, Defined
Mean is the arithmetic average: add every value and divide by how many there are. It uses every single data point, which makes it statistically efficient โ but also means a single extreme value can pull it substantially off-centre.
Median is the middle value once the data is sorted โ or the average of the two middle values if there's an even number of data points. Because it only cares about rank, not magnitude, a single enormous outlier moves the median by at most one position, not by its full size.
Mode is simply the most frequently occurring value. It's the only one of the three that makes sense for non-numeric (categorical) data โ "red" can be the mode of a list of car colours, but it can't have a mean.
Worked Example, Fully Shown
Problem: A small team's weekly sales figures (in thousands) are 20, 22, 24, 25, and 180 โ one unusually large week. Find the mean, median, and mode.
Mean: (20+22+24+25+180)/5 = 271/5 = 54.2
Median (sorted: 20, 22, 24, 25, 180): the middle value is 24
Mode: none โ every value occurs exactly once
Notice the gap: the mean (54.2) is more than double the median (24), entirely because of that one 180 week. If you had to describe "a typical week" for this team, the median โ 24 โ is by far the more honest answer; the mean is being dragged upward by a single outlier that isn't representative of most weeks.
When to Use Each One
Use the mean when the data is roughly symmetric and you want a measure that accounts for every value โ test score averages, average daily temperatures, average transaction size on a typical day.
Use the median for skewed data or anything prone to extreme outliers โ household income, house prices, CEO pay, response times. News reports on "median household income" rather than mean income for exactly this reason: a handful of very high earners would otherwise make the "average" household look far richer than it actually is.
Use the mode for categorical data (most common product size, most common survey answer) or when you specifically care about "what happens most often" rather than a mathematical centre โ a shoe store cares more about which size sells most (the mode) than the mean shoe size, which might not correspond to a size that exists.
How the Gap Between Mean and Median Reveals Skew
As a rule of thumb: if the mean is noticeably larger than the median, the data is right-skewed (a long tail of unusually high values, like income). If the mean is noticeably smaller than the median, the data is left-skewed (a long tail of unusually low values). When mean and median are close together, the data is roughly symmetric. This is a quick, practical diagnostic โ for a precise measure of skew, see our skewness & kurtosis calculator.