Mean, Median, Mode Calculator
Paste a list of numbers and get all three averages plus the spread. Sample and population versions are both shown, because using the wrong one is the usual source of a wrong answer.
How it works
How the Mean, Median, Mode Calculator works
the part a result on its own leaves out
Three averages, three questions
The mean balances the values, the median splits them in half, and the mode is the one that occurs most. They answer different questions, and on skewed data they disagree — which is information, not a problem.
Why there are two standard deviations
Dividing by n describes the data you have. Dividing by n − 1 estimates the spread of the wider population the data came from, correcting for the fact that a sample sits closer to its own mean than to the true one.
Common mistakes
Common mistakes with mean, median, mode
the errors that actually show up, not every possible slip
Finding the median without sorting
The median is the middle value of the ordered list. Taking the middle of the list as typed gives a number that means nothing.
Using the population formula on a sample
If the data is a sample, divide by n − 1. Using n understates the spread, and on small samples the difference is large.
Reporting a mode that is not there
If every value appears exactly once there is no mode. Naming one anyway invents a pattern the data does not have.
Questions
Asked often enough to answer here
answers that change how you work
When should I use the median instead of the mean?
When outliers would distort the answer. One very high salary pulls the mean upward while the median stays where most people are, which is why income is reported as a median.
Can a data set have more than one mode?
Yes. If two values tie for most frequent, the set is bimodal and both are listed.
What does standard deviation actually tell me?
The typical distance of a value from the mean, in the original units. A small one means the data clusters; a large one means it is spread out.
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