How this calculator works
The mean spreads the total equally across all observations. The median splits an ordered list at its centre and averages the two central values for even n. Modes are the values tied for the greatest repeated frequency. This tool uses the common classroom convention of no mode when every distinct value appears once. The frequency table makes repeated values and tied modes visible.
Formula
mean = Σx/n; odd-n median = x((n + 1)/2); even-n median = (x(n/2) + x(n/2 + 1))/2. Modes maximise frequency.
Worked example
For 1, 2, 2, 5, the mean is 10/4 = 2.5, the median is (2 + 2)/2 = 2 and the mode is 2.
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Frequently asked questions
Which centre should I report?
The mean responds to every value, while the median is less sensitive to distant extremes. Choose based on the question and distribution.
Can there be two modes?
Yes. For 1, 1, 3, 3, both 1 and 3 appear twice and are reported together.
Can I enter weights?
This page treats each list entry as one observation. For frequency-weighted values, use the grouped-data tool with actual values as midpoints.