The three measures of central tendency, plus range — with worked steps
Type your data below to find the mean, median and mode at once, along with the range and a step-by-step solution.
The share link reproduces your exact data and settings — paste it in an email, chat, or assignment and anyone who opens it sees the same results.
Saved to this device only (browser local storage). Use a share link to move data between devices.
These are the three common measures of central tendency — different ways of describing the "typical" value in a data set. The mean is the arithmetic average: add every value and divide by how many there are. The median is the middle value once the data is sorted (or the average of the two middle values when the count is even). The mode is the value that appears most often; a data set can have one mode, several, or none.
The mean uses every value and works well for roughly symmetric data, but it is pulled toward extreme values. The median ignores how far away the extremes are, so it is the more robust choice for skewed data or data with outliers — which is why median household income is usually reported instead of the mean. The mode is most useful for categorical or discrete data, such as the most common shoe size sold.
Consider salaries where most people earn a modest amount but one person earns a fortune. The mean is dragged upward by that single large value and overstates the typical salary, while the median stays near the bulk of the data. Comparing the mean and median is a quick way to detect skew: if the mean is much higher than the median, the data is right-skewed.
The mean is the arithmetic average of all values; the median is the middle value when the data is sorted. The median is less affected by outliers, so it better represents skewed data.
Yes. If two or more values tie for the highest frequency, the set is bimodal or multimodal. If no value repeats, there is no mode. This calculator lists all modes it finds.
The range is the difference between the largest and smallest values. It is the simplest measure of spread and is shown in the additional statistics above.