Mean Median Mode Calculator
Mean, median, mode, and range from a list of numbers.
Input sheet
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Mean, median, and mode are the three classic "averages," each summarizing a data set in a different way. Add the range and you have a quick statistical snapshot of any list of numbers.
How it works
Mean = sum ÷ count. Median is the middle value (or the average of the two middle values). Mode is the most frequent value; range is max − min.
The mean is the arithmetic average — add everything up and divide by how many values there are. The median is the middle value after sorting, which is far more resistant to extreme outliers than the mean. The mode is the value that appears most often, useful for categorical or repeated data.
When the list has an even count, there's no single middle value, so the median is the average of the two central numbers. If no value repeats more than the others, there is no mode and the result shows 'none'. The range — maximum minus minimum — measures how spread out the data is.
Mean = sum of values ÷ count. Median = middle value of the sorted list (or the average of the two middle values for an even count). Mode = most frequently occurring value. Range = maximum − minimum.
Worked examples
The list 4, 8, 15, 16, 23, 42 (the default). → Mean 18.00, median 15.5, mode none, range 38, count 6
Sum is 108 over 6 values, so mean = 18. With an even count, the median averages the two middle values (15 and 16) to 15.5. No value repeats, so mode is 'none'. Range = 42 − 4 = 38.
The list 2, 5, 5, 7, 9. → Mean 5.60, median 5, mode 5, range 7, count 5
Sum is 28 over 5 values, so mean = 5.6. Sorted, the middle value is 5. The value 5 appears twice (more than any other), so mode = 5. Range = 9 − 2 = 7.
Tips & gotchas
- When a few extreme values skew your data (incomes, home prices), trust the median over the mean — the median ignores how far out the outliers sit.
- A data set can have more than one mode; this tool reports the single most frequent value, so be aware if your data is genuinely multi-modal.
- Separate every number with a comma; non-numeric entries are ignored, so stray text won't break the calculation but also won't be counted.
- Compare the mean and median: if they're far apart, your data is skewed; if they're close, it's roughly symmetric.
FAQ
What if no value repeats?
Then there is no mode and the result shows 'none'.
Which average should I actually use?
Use the mean for symmetric data, the median when outliers would distort the picture, and the mode when you care about the most common value.
How is the median found when there's an even number of values?
There's no single middle value, so the median is the average of the two central numbers after sorting.
What does the range tell me?
The range (maximum minus minimum) is the simplest measure of spread, showing the full width between your smallest and largest values.
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