Central tendency
What do mean, median, and mode describe?
Mean, median, and mode are measures of central tendency. Each describes the center of a dataset in a different way.
Mean
Calculate the arithmetic average
Meanx̄ = Σx ÷ n
Add all values and divide by the number of values. The mean uses every observation, so extreme values can strongly affect it.
Median
Find the middle of the sorted dataset
Sort the values from smallest to largest. With an odd number of values, choose the middle value. With an even number, average the two middle values.
Mode
Identify the most frequent value
The mode is the value that occurs most frequently. A dataset may have one mode, multiple modes, or no mode.
Worked example
Analyze 2, 4, 4, 6, and 8
- Sum: 2 + 4 + 4 + 6 + 8 = 24.
- Mean: 24 ÷ 5 = 4.8.
- Median: the middle sorted value is 4.
- Mode: 4 occurs most often, so the mode is 4.
- Range: 8 − 2 = 6.
Choosing a measure
Which measure should you report?
Mean
Uses every value
Useful for balanced numerical datasets, but sensitive to unusually high or low values.
Median
Resistant to extremes
Useful when the dataset is skewed or contains unusually large or small values.
Mode
Shows the most common value
Useful for identifying the most frequent result or category.
Laboratory use
Summarize repeated measurements
Mean is commonly used to summarize repeated measurements, while median can be useful when a dataset contains an extreme result.
For a fuller evaluation of spread and consistency, use the Standard Deviation Calculator.
Data interpretation
Put the statistics in context
A summary statistic should be interpreted together with sample size, spread, units, anomalies, and the experimental method.
Review the experimental results analysis guide for a complete workflow.
Interpretation limits
Assumptions and limitations
Mean, median, and mode summarize a dataset but do not fully describe its spread, shape, uncertainty, or measurement quality. Each statistic can emphasize a different feature of the same data.
The mean is sensitive to extreme values, the median does not show variability, and a dataset may have no mode or more than one mode. Conclusions should therefore consider the data distribution and context.
Related tools
Related statistics calculators
Measure how widely observations vary around their mean with the Standard Deviation Calculator.
Fit a straight-line relationship to paired observations with the Linear Regression Calculator.
Questions and answers
Mean, median, and mode FAQ
How is the mean calculated?
The mean is calculated by adding all values and dividing the sum by the total number of values.
How is the median calculated?
The values are sorted from smallest to largest. For an odd number of values, the median is the middle value. For an even number, it is the mean of the two middle values.
Can a dataset have more than one mode?
Yes. A dataset is multimodal when two or more values share the highest frequency.
What happens when every value occurs once?
The dataset has no mode because no value occurs more frequently than the others.