Quick answer
The mean is Σx ÷ n, the median is the middle value (the average of the two middle values when n is even) and the mode is the most frequent value. For 4, 8, 15, 16, 23, 42: mean 18, median 15.5, no mode, count 6.
Enter a list of numbers. The calculator returns the mean, median, mode and count.
Related tools: Mean Calculator: Mean of a data set. Standard Deviation Calculator: Sample or population standard deviation with variance and mean. Z-Score Calculator: Standardize a value using a mean and standard deviation.
How to use the Mean Median Mode Calculator
- Type data set, for example 4, 8, 15, 16, 23, 42.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Data set | Text, such as 4, 8, 15, 16, 23, 42 | — |
Formula and method
Formula
mean = Σx ÷ n; median = middle value (average of the two middle values when n is even); mode = most frequent value(s)
IEEE-754 double precision; shown to at most 6 decimal places.
Sort the data for the median; count frequencies for the mode. No mode is reported when every value is unique.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Data set = 4, 8, 15, 16, 23, 42.
| Result | Value |
|---|---|
| Mean | 18 |
| Median | 15.5 |
| Mode | None |
| Count | 6 |
Example 2
Inputs: Data set = 1 2 2 3 3 4.
| Result | Value |
|---|---|
| Mean | 2.5 |
| Median | 2.5 |
| Mode | 2, 3 |
| Count | 6 |
Example 3
Inputs: Data set = 7.
| Result | Value |
|---|---|
| Mean | 7 |
| Median | 7 |
| Mode | None |
| Count | 1 |
The first line is the headline result (mean). Below it the mean Median Mode Calculator lists median, mode and count, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Why they differ
The mean of 18 is pulled above the median of 15.5 by the 42. When the mean exceeds the median, the data are right-skewed. All values are distinct here, so there is no mode.
Mode details
If all values occur once, there is no mode; if several tie, all are listed. For the range as well, see the Mean Median Mode Range Calculator. Mode suits categorical or discrete data.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Data set: left empty shows "Enter data set." beside that field and no result.
Choosing between the Mean Median Mode Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Mean Calculator](/statistics/mean/) | data set | Mean |
| [Standard Deviation Calculator](/statistics/standard-deviation-calculator/) | data set and data type | Population standard deviation (σ) |
| [Z-Score Calculator](/statistics/z-score-calculator/) | value, mean and standard deviation | Z-score |
| [Confidence Interval Calculator](/statistics/confidence-interval-calculator/) | sample mean, standard deviation and sample size | Confidence interval |
| [Mean Median Mode Range Calculator](/statistics/mean-median-mode-range-calculator/) | data set | Mean |
Background: descriptive statistics
Population statistics divide by n and sample statistics divide by n − 1 (Bessel's correction), because a sample tends to understate variability. Use the population version when your data is every value in the group, and the sample version when it is a subset.
Defaults differ between tools, and so do quartile conventions, which can give slightly different values for small data sets; this page states the method it uses.
Assumptions and limitations
- No mode when all values occur once
- Multiple modes are all listed
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for data set to confirm this.
Frequently asked questions
What is the median of 1, 3, 5, 7?
For 1, 3, 5, 7 the median is the average of the middle two: (3 + 5) ÷ 2 = 4.
Can there be two modes?
Yes. If two values tie for the highest frequency the data are bimodal, as with 1, 2, 2, 3, 3, 4.
Which average is best?
It depends on the shape.
What does the Mean Median Mode Calculator calculate?
Mean, median and mode of a data set. It returns Mean, Median, Mode and Count.
What formula does the Mean Median Mode Calculator use?
mean = Σx ÷ n; median = middle value (average of the two middle values when n is even); mode = most frequent value(s). Sort the data for the median; count frequencies for the mode.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. No mode when all values occur once.
What are the limits of this calculator?
No mode when all values occur once. Multiple modes are all listed.
What is an example of a mean Median Mode result?
With data set 4, 8, 15, 16, 23, 42, the mean is 18.
Related calculators
- Mean Calculator — Mean of a data set.
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Z-Score Calculator — Standardize a value using a mean and standard deviation.
- Confidence Interval Calculator — Confidence interval for a mean (t or z).
- Mean Median Mode Range Calculator — Mean, median, mode and range of a data set.
- Median Calculator — Median of a data set.
- Mode Calculator — Mode of a data set.
- Geometric Mean Calculator — Geometric mean of a data set.
- Quartile Calculator — Quartiles of a data set.
Sources
- Standard statistics definition (e.g. NIST/SEMATECH e-Handbook of Statistical Methods)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.