Understanding your result
The mean divides the sum by the count. The median uses the middle sorted value or the average of the two middle values. The mode lists every value tied for the highest repeated frequency.
To measure how widely the values vary around the mean, use the Standard Deviation Calculator with the same dataset.
For the chance of a specified number of successes in independent trials, the Probability Calculator provides a binomial model rather than a summary of observed values.
The formula
Median and mode describe the center differently from the mean. Sorting affects the median calculation but does not change the underlying dataset.
A five-value dataset
For 1, 2, 2, 4, 6, the sum is 15 and mean is 3. The sorted middle value is 2, the repeated mode is 2, and the range is 5.
How to use this calculator
- Paste or type numbers separated by commas, spaces, or semicolons.
- Calculate the six descriptive statistics.
- Compare mean, median, and mode before choosing a representative center.
The mean can respond strongly to extremes
Every value contributes to the arithmetic mean, so one unusually high or low observation can move it substantially.
The median depends on position after sorting and can better describe a skewed distribution, though context determines which measure is useful.
A dataset may have several modes
If multiple values share the highest repeated frequency, each is reported as a mode.
When every value appears once, this calculator reports no repeated mode rather than declaring every observation a mode.
Assumptions & limitations
What this calculation assumes
- Each token represents one observation.
- All observations have equal weight.
- Mode comparison uses exact entered numeric values.
What to keep in mind
- The calculator accepts at most 10,000 values.
- Rounded measurements that look similar can remain distinct values.
- These summaries do not describe distribution shape or uncertainty.
Common questions
Is average the same as mean?
In common usage average often means arithmetic mean, though average can refer to other measures in some contexts.
How is median calculated for an even count?
The two middle sorted values are added and divided by two.
Can there be more than one mode?
Yes. Every value tied for the highest repeated count is listed.