Calculator tool
How this calculator works
Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.
Four different summaries
The calculator reports several descriptive statistics because one number rarely tells the whole story. The mean is the arithmetic average. The median is the middle value after sorting. The mode is the most frequent value. The range is the maximum minus the minimum.
For the values 2, 4, 7, 7, 9, the mean is 5.8, the median is 7, the mode is 7, and the range is 7. Each statistic answers a different question: center, middle position, repetition, or spread.
Why they can disagree
An outlier can pull the mean while leaving the median almost unchanged. A data set may have no mode when every value appears only once, or more than one mode when frequencies tie. Use the group together when summarizing a small set rather than treating the mean as the only useful description.
Frequently asked questions
When is median more useful than mean?
Median is often more useful when extreme values distort the average, such as income or home-price data with a few unusually large observations.
Can a data set have no mode?
Yes. If every value appears the same number of times and no value repeats, the calculator reports no mode.
What does range miss?
Range uses only the minimum and maximum. It does not show how the rest of the values are distributed between them.
Why sort the data for the median?
Because the median is positional. You need the ordered list before you can identify the central value or central pair.
