Mean, Median, Mode Calculator
Enter a list of numbers to find the mean, median, mode, range, count, sum, and standard deviation of your data set, with clear steps.
- Count the values and add them: 6 numbers, sum 108.
- Mean = sum / count = 108 / 6 = 18.
- Sort the values and take the middle for the median: 15.5.
- Every value appears once, so there is no mode.
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All calculations run locally in your browser. Your entered values are not sent to an external service.
How to Use the Mean, Median, Mode Calculator
Type or paste your numbers into the data box, separated by commas, spaces, or new lines, and select Calculate. The tool reports the mean, median, mode, and other summary statistics with the steps used.
- Enter every value in your data set.
- Select Calculate to see the averages and spread.
- Review the count, sum, range, and standard deviation for more context.
Values can be decimals or negatives. The standard deviation shown is the population standard deviation, which divides by the number of values. For sample versus population steps, use the Standard Deviation Calculator. To standardize one score after you have μ and σ, use the Z-Score Calculator. For values that should not count equally, use the Weighted Average Calculator.
Mean, Median, and Mode
The mean, or average, adds every value and divides by how many there are. It uses all the data but is sensitive to extreme values.
The median is the middle value after sorting. With an even count, it is the average of the two middle values. The median is resistant to outliers, which makes it useful for skewed data such as incomes.
The mode is the value that appears most often. A data set can have one mode, several modes, or no mode when every value is unique. The mode is the only average that also works for non-numeric categories.
Mean, Median, Mode Examples
No repeated values
For 4, 8, 15, 16, 23, 42, the sum is 108 and the count is 6, so the mean is 18. Sorted, the two middle values are 15 and 16, so the median is 15.5. Every value is unique, so there is no mode.
A clear mode
For 7, 7, 8, 9, 10, 10, 10, 12, the value 10 appears three times, so the mode is 10. The mean is about 9.13 and the median is 9.5.
Effect of an outlier
Adding a value of 200 to a small data set raises the mean sharply but changes the median only slightly. This is why the median is often reported for skewed data.
Which Average Should You Use?
Use the mean for roughly symmetric data without extreme outliers, such as test scores in a normal range. Use the median when the data is skewed or contains outliers, such as house prices or salaries, because it better represents a typical value. Use the mode for the most common category or repeated measurement, and when the data is not numeric.
Reporting more than one measure often tells a fuller story. The mean and median together reveal skew: when the mean is much larger than the median, the data has a long tail toward high values.
Common Mistakes
Forgetting to sort before finding the median
The median is the middle of the sorted values, not the middle of the original order.
Averaging the two middle values incorrectly
With an even count, add the two middle values and divide by two.
Assuming there is always one mode
A data set can have no mode or several modes. All values with the highest frequency are modes.
Letting an outlier distort the mean
A single extreme value can pull the mean far from a typical value. Consider the median as well.
Confusing population and sample statistics
This tool uses the population standard deviation. A sample standard deviation divides by n − 1 instead of n.
Mean, Median, Mode FAQs
What is the difference between mean, median, and mode?
The mean is the average, the median is the middle value when sorted, and the mode is the most frequent value.
How do I find the median of an even number of values?
Sort the values and average the two middle numbers.
Can a data set have more than one mode?
Yes. If several values share the highest frequency, the data set is multimodal and all of them are modes.
What if there is no repeated value?
Then there is no mode, because no value occurs more often than the others.
Which standard deviation does this use?
The population standard deviation, which divides the sum of squared deviations by the number of values. Use the Standard Deviation Calculator to compare sample s and population σ with the squared-deviation steps.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
Sources
Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.