Mean Median Mode Calculator
Calculate measures of central tendency and range for any set of numbers.
Want the median worked step by step, with quartiles? Median calculator →
Three averages that disagree for a reason
The mean is the total divided by the count. The median is the middle value once sorted — the average of the two middle values when the count is even. Themode is the most frequent value, and a dataset can have none, one, or several. They answer different questions, and the gap between them is itself informative.
The mean is sensitive to outliers; the median is not. Take five salaries of 30k, 32k, 35k, 36k and 500k: the mean is over 126k and describes nobody, while the median is 35k and describes the group well. This is why income and house prices are almost always reported as medians — a handful of extreme values would otherwise drag the mean somewhere unrepresentative.
Comparing them diagnoses the shape of the data. Mean and median roughly equal suggests symmetry. Mean well above median means a right skew, with a long tail of high values. Mean below median means a left skew. The mode is the only one that works on categorical data — you can find the most common colour, but not its average. Where the mean is misleading and you still want to use one, check the skew first.
Frequently Asked Questions
What is the difference between Mean, Median, and Mode?
Mean is the average (sum / count). Median is the middle value when sorted. Mode is the most frequently occurring value.
What if a data set has multiple modes or no mode?
If all values occur with frequency 1, there is no mode. If multiple values tie for highest frequency, the set is multimodal.
Can a data set have more than one mode?
Yes. A set with two equally frequent peaks is bimodal, and more are multimodal; a set where every value appears once has no mode at all. Multimodality often signals that two different populations have been mixed together, which is useful diagnostic information the mean would hide.
What is the range and why is it limited?
The range is the largest value minus the smallest. It is easy to compute but depends entirely on the two most extreme observations, so a single outlier dominates it. Interquartile range and standard deviation describe spread far more robustly.