Mean, Median & Mode
Central tendency from a list of numbers.
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Formula
Mean = sum ÷ count; Median = middle value (or average of two middles); Mode = most frequent value
The mean is the arithmetic average. The median is the middle value after sorting (or the average of the two central values when the count is even). The mode is the value that appears most often; if every value is unique, there is no mode.
Worked example
For 10, 20, 20, and 30 the mean is 20, the median is also 20 (the average of the two middle values), and the mode is 20 because it appears twice.
Where this can give the wrong answer
- With an even number of values, the median is the average of the two middle numbers — for 10, 20, 30, 40 the median is 25, not 20 or 30.
- When every value appears exactly once, the calculator reports 'No mode (all values unique)' rather than picking an arbitrary value.
- If two or more values tie for highest frequency, all of them are listed as modes — the data is called multimodal.
FAQ
- Use the mean for symmetric, well-behaved data. Prefer the median when outliers skew the average (e.g. house prices). The mode is best for categorical or discrete data where 'most common' is the question — like shoe size or survey responses.