Mean, Median, Mode Calculator
Paste or type a list of numbers to find the mean, median, mode and range, with the working shown.
Mean, median and mode are three measures of the center of a data set. The mean is the sum divided by the count; the median is the middle value when the data is sorted; the mode is the most frequent value. For 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5, the median is 4.5, and the mode is 4.
How to Use This Calculator
Type or paste your numbers into the box, separated by commas, spaces or line breaks. The calculator returns the mean, median, mode and range at once, so you can see the center of your data three different ways plus how spread out it is.
All three are 'averages' but they answer slightly different questions, and comparing them is often more informative than any one alone. When the mean and median are close, the data is fairly symmetric; when they differ a lot, the data is skewed or has outliers pulling the mean.
How the Calculation Works
The mean adds all the values and divides by how many there are. The median sorts the values and takes the middle one; if there is an even count, it averages the two middle values. The mode is the value that appears most often — a data set can have one mode, several (if multiple values tie for most frequent), or none (if every value is unique). The range, shown in the working, is simply the largest value minus the smallest.
Worked Example
Take 2, 4, 4, 4, 5, 5, 7, 9. Mean = (2+4+4+4+5+5+7+9) ÷ 8 = 40 ÷ 8 = 5. Sorted, the two middle values (positions 4 and 5) are 4 and 5, so the median = (4+5) ÷ 2 = 4.5. The value 4 appears three times, more than any other, so the mode = 4. The range is 9 − 2 = 7. Here the mean (5) sits a little above the median (4.5), a mild sign of right skew from the value 9.
What the Result Means
The mean is the balancing point of the data and uses every value, but it is pulled by outliers. The median is the true middle and is resistant to outliers, which makes it the better 'typical value' for skewed data like incomes or house prices. The mode identifies the most common outcome, useful for categorical or discrete data. Reading all three together reveals shape: mean ≈ median suggests symmetry, mean > median suggests a right (high) skew, and mean < median suggests a left (low) skew.
Assumptions and Limitations
These measures apply to numeric data entered as a list; the mode also makes sense for repeated discrete values. The mean is sensitive to outliers and can be misleading for skewed distributions, where the median is usually preferred. A data set may legitimately have no mode (all values unique) or several modes. The calculations are exact for the numbers you provide; results are only as meaningful as the data is clean and complete.
Who Uses a Mean, Median, Mode Calculator
Students, teachers, and anyone with a list of numbers use this to get the mean, median, mode, and range at once. Run it to summarize a data set, complete homework, or judge whether an average is being skewed by outliers. Paste your numbers to see all four measures.
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Open calculator →Frequently Asked Questions
What is the difference between mean, median and mode?
The mean is the arithmetic average (sum ÷ count), the median is the middle value when sorted, and the mode is the most frequent value. They can all differ, especially in skewed data.
When should I use the median instead of the mean?
Use the median when the data is skewed or has outliers, such as incomes or home prices. The median is not distorted by a few extreme values, so it better represents the typical case.
Can a data set have more than one mode?
Yes. If two or more values tie for the highest frequency, the data is multimodal and has several modes. If every value appears once, there is no mode.
How do I find the median of an even number of values?
Sort the values and average the two middle ones. For eight values, average the 4th and 5th after sorting. For an odd count, the single middle value is the median.
What does it mean if the mean is higher than the median?
It usually indicates a right-skewed distribution — a tail of larger values pulls the mean above the median. If the mean is lower than the median, the data is left-skewed.
What is the range?
The range is the difference between the largest and smallest values, a simple measure of spread. This calculator shows it alongside the averages in the working.
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