Mean, Median, Mode, Range CalculatorFree online math calculator — instant results, no sign-up
Central tendency and spread of a list.
About the Mean, Median, Mode, Range Calculator
This calculator computes the primary measures of central tendency (mean, median, and mode) along with the statistical spread (range) for an arbitrary list of numerical values. It is commonly used by students, researchers, and data analysts to summarize the distribution and central location of a dataset.
- Numbers
- A comma-separated, space-separated, or line-delimited set of real numbers (e.g., 3, 7, 7, 2, 9, 4, 7, 1).
Formula and method
Mean = (∑ x) / n; Median = x_((n+1)/2) if n is odd, or (x_(n/2) + x_(n/2 + 1)) / 2 if n is even (on sorted data); Mode = value(s) with highest frequency count > 1; Range = max(x) − min(x)
- ∑ xSum of all numerical values in the dataset
- nTotal count of values in the dataset
- max(x)Maximum value in the dataset
- min(x)Minimum value in the dataset
The tool parses the input string into a list of numbers, computes the arithmetic mean formatted to up to six decimal places, and sorts the list to find the median. It constructs a frequency map to identify any mode values appearing more than once (returning 'None' if all values appear only once), and subtracts the minimum value from the maximum value to find the range.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Numbers3, 7, 7, 2, 9, 4, 7, 1
Results
- Mean5
- Median5.5
- Mode7
- Range8
How to use the Mean, Median, Mode, Range Calculator
- 1Parse the input text to extract all valid numeric values and determine the count n.
- 2Sum all numbers and divide by n to calculate the arithmetic mean.
- 3Sort the values in ascending order to find the middle value (or the average of the two middle values) for the median.
- 4Count value frequencies to identify any recurring modes (frequency > 1) and calculate the range as maximum minus minimum.
Reading your result
The mean and median indicate where the center of the data lies; large discrepancies between them often indicate skewness or extreme outliers. The mode identifies the most frequently recurring number, while the range shows the total span from the smallest to the largest observation.
Limitations
The range relies solely on the two extreme values and does not reflect data variability between them or adjust for outliers. Additionally, the tool requires at least one value to repeat (frequency greater than 1) to identify a mode, displaying 'None' if all numbers occur with equal frequency of 1.
Common questions
Why does the calculator return 'None' for the mode?+
A mode is only reported when at least one number appears more than once. If every number in your dataset occurs with equal frequency of one, there is no single peak or modal value.
Can there be multiple modes in a dataset?+
Yes. If two or more numbers tie for the highest occurrence count and appear at least twice, the calculator displays all of them separated by commas (multimodal distribution).
How does an outlier affect the mean versus the median?+
The arithmetic mean incorporates every data point, making it sensitive to extreme values. The median relies purely on positional ranking, making it resistant to outliers.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.