Mean or median: what does each number tell you?

Two indicators can describe the same series and tell different stories. The choice depends on the question asked.

The mean accounts for every value

The mean is obtained by adding all values and dividing by their number. For the series 10, 12, 14, 16 and 18, the sum is 70 and the mean is 14. Each value contributes to the result. If one value becomes very large, it can substantially shift the mean even when the other numbers do not change.

The median looks at the central position

To find the median, first sort the numbers. For an odd number of values, take the middle one. The median of 10, 12, 14, 16 and 100 remains 14, while the mean becomes 30.4. The median therefore resists a single very high value better. For an even number of values, our tool averages the two central values: for 10, 12, 16 and 18, the median is 14.

Also observe spread

Two series can have the same mean while being very different. The values 14, 14 and 14 have the same mean as 4, 14 and 24, but are much less spread out. The range, the difference between maximum and minimum, provides an initial guide. Standard deviation describes differences from the mean more broadly. The tool uses a population formula divided by N, not a sample estimate divided by N − 1.

Explain the choice in your conclusion

The mean is often useful for describing a total quantity divided equally. To locate a central value when a series contains extremes, the median provides complementary information. Present both when their difference helps explain the data. Also check units, missing values and entry errors. No isolated indicator replaces examining the series and how it was collected.

Put it into practice

• Arithmetic mean
• Median
• Population standard deviation

Educational text prepared with AI assistance. The examples use adjustable assumptions and are not personal advice.