Mean, Median, Mode & Range Calculator
Calculate the mean, median, mode, and range of a list of numbers.
Try an example
5.6667
About this calculator
Mean, Median, Mode and Range Explained
These four numbers summarize a list of values in different ways, and together they give a quick picture of any data set. Enter your numbers separated by commas and this calculator returns the mean, median, mode and range at once, along with the count and the sum. They are the first tools of descriptive statistics, used in school, science, business and everyday decisions.
Mean (the Average)
The mean is the sum of all values divided by how many there are: mean = Σx ÷ n. It is usually what people mean by "average." For 10, 2, 38, 23, 38, 23, 21 the sum is 155 and there are 7 values, so the mean is about 22.14. The mean uses every value, which makes it sensitive to extreme numbers — one very large entry can drag it far from the typical value. In statistics the sample mean is written x̄ ("x bar") and the population mean is written μ.
Median (the Middle Value)
The median is the middle number once the data is sorted. With an odd count it is the center value; with an even count it is the average of the two middle values. Sorting the example gives 2, 10, 21, 23, 23, 38, 38, so the median is 23. Because the median ignores how large the extremes are, it is the better measure of "typical" for skewed data such as incomes or house prices.
Mode (the Most Common Value)
The mode is the value that appears most often. A data set can have one mode, several modes (23 and 38 both appear twice above), or none if every value is unique. It is the only one of the three that works for non-numeric categories — such as the most common shoe size or favorite color.
Range (the Spread)
Range = largest value − smallest value. In the example it is 38 − 2 = 36. The range tells you how spread out the data is, though it depends on just two numbers; for a fuller view of variation, pair it with the Standard Deviation Calculator.
Which One Should You Use?
- Use the mean for evenly distributed data with no big outliers.
- Use the median when the data is skewed or has outliers.
- Use the mode for categories or to find the most frequent value.
- Report the range alongside any of them to show how much the values vary.
Looking at all four together is the safest habit: when the mean and the median differ a lot, that is a sign the data is skewed.
Worked example
For the list 4, 8, 6, 5, 3, 8: the mean is 34 ÷ 6 = 5.6667, the median (average of the two middle values 5 and 6 once sorted) is 5.5, the mode is 8 (it appears twice, more than any other value), and the range is 8 − 3 = 5.
Frequently asked questions
What's the difference between mean, median, and mode?
The mean is the arithmetic average; the median is the middle value when the numbers are sorted; the mode is the value that appears most often. Each describes "the middle" differently, and they can all give different answers for the same data.
Why use the median instead of the mean?
The median is less sensitive to outliers — a single very large or small value can pull the mean far from where most of the data actually sits, but barely moves the median.
What if there's more than one mode?
A data set can have multiple modes if two or more values tie for the highest frequency — this calculator lists all of them. If every value appears exactly once, there's no mode.
How is the median calculated for an even-length list?
It's the average of the two middle values once the list is sorted — for an odd-length list, it's simply the single middle value.
