Mean Median Mode Calculator
Give this calculator any list of numbers and it returns the mean, median and mode together, with every step shown: the sorted data, the full addition for the mean, a frequency table, quartiles, both standard deviations and an outlier check. It is a central-tendency summary of raw data. If instead you have outcomes with probabilities and want the mean of a probability distribution, that is the separate mean of distribution calculator.
Quartiles use Tukey hinges: Q1 is the median of the lower half and Q3 the median of the upper half of the sorted data. Outliers are flagged with Tukey fences at 1.5 × IQR beyond the quartiles.
Quick Answer
For the data set 2, 4, 6, 8, 10, 7, 7, the mean is 6.2857, the median is 7 and the mode is 7. The range is 8, the quartiles are Q1 = 4 and Q3 = 8, and the population standard deviation is 2.4328. Paste your own numbers into the calculator above and every one of those figures comes back with the full working shown.
Key takeaways
- Mean, median and mode are three different “centers”: the arithmetic average, the middle value of the sorted list, and the most frequent value. On the worked example they are 6.2857, 7 and 7.
- When the mean sits below the median, the data leans left; when it sits above, it leans right. The gap between them is itself a skew signal, and the calculator labels it for you.
- Quartiles here use Tukey hinges: the median is excluded from each half when the count is odd, so Q1 and Q3 are the medians of the two halves. Outliers are flagged at 1.5 × IQR beyond the quartiles, the same fences box plots use.
- Both standard deviations are reported. Use the population figure (÷ n) when your numbers are the whole group, and the sample figure (÷ n − 1) when they are a sample of something larger.
- Quick Answer
- How to use the mean, median and mode calculator
- Formulas: mean, median, mode, quartiles and standard deviation
- Worked example: seven numbers, checked end to end
- Which average should you use?
- Skew, quartiles and outliers: reading the rest of the output
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the mean, median and mode calculator
Paste a list of numbers, click Calculate, and read the three headline figures plus a full statistics table. The results stay hidden until you calculate.
- Paste or type your numbers: commas, spaces, semicolons, pipes and line breaks all work, so a column copied from a spreadsheet pastes straight in. The worked example 2, 4, 6, 8, 10, 7, 7 is pre-filled.
- Read the three headline numbers: mean, median and mode appear at 32px at the top, with count, sum, range, quartiles, variances and both standard deviations in the table beneath.
- Check the working: the sorted list, a frequency table and a numbered “How it was calculated” list show every step, so you can verify the arithmetic by hand or in class.
- Read the distribution note: the calculator labels the skew (mean versus median) and flags any outliers by the 1.5 × IQR rule. Anything that is not a number is skipped and counted in the note rather than silently treated as zero.
Formulas: mean, median, mode, quartiles and standard deviation
The mean is the sum of all values divided by how many there are. The median is the middle value of the sorted list, or the average of the two middle values when the count is even. The mode is the value that occurs most often, and there is no mode when every value appears exactly once.
Median = middle of the sorted values (average of the two middle values for even n)
Mode = value with the highest frequency; “No mode” if all frequencies are 1
Q1, Q3 = medians of the lower and upper halves (Tukey hinges)
IQR = Q3 − Q1 | Outlier fences = Q1 − 1.5×IQR and Q3 + 1.5×IQR
Population SD = √[Σ(x − mean)² ÷ n] | Sample SD = √[Σ(x − mean)² ÷ (n − 1)]
The quartile method deserves a sentence because rival tools quietly disagree about it. This calculator uses Tukey hinges: with an odd count the median value itself is excluded before each half is median-ed; with an even count the halves are exact. The NIST/SEMATECH e-Handbook’s measures of location page explains why the median resists distortion from extreme values while the mean does not, and the OpenStax chapter on measures of center works through the same mean, median and mode definitions with classroom examples.
Worked example: seven numbers, checked end to end
The pre-filled data set is 2, 4, 6, 8, 10, 7, 7. Running it gives a mean of 6.2857, a median of 7 and a mode of 7, and the calculator’s own step list walks the same path:
Quartiles: splitting the sorted list around the median gives the lower half 2, 4, 6 and the upper half 7, 8, 10, so Q1 = 4 and Q3 = 8, with an interquartile range of 4. The population variance is 5.9184, so the population standard deviation is 2.4328 (sample: 2.6277). Because the mean sits below the median, the distribution reads as left-skewed, and no outliers trip the 1.5 × IQR fences. Type these numbers in and you get the identical figures back, to the fourth decimal.
Four more data sets, run through the same tool, to show the edges:
| Data set | Mean | Median | Mode |
|---|---|---|---|
| 5, 10, 15, 20, 25, 10, 30 | 16.4286 | 15 | 10 |
| 2, 2, 3, 3, 4 (bimodal) | 2.8 | 3 | 2, 3 |
| -5, -2.5, 0, 3.75, 100 | 19.25 | 0 | No mode |
| 5, 5, 5, 5 | 5 | 5 | 5 |
Notice the third row: a single value of 100 drags the mean to 19.25 while the median stays at 0. That is the textbook reason the median is the resistant measure, and it is exactly the behaviour the NIST handbook demonstrates with its Cauchy-distribution example.
Which average should you use?
Use the mean when every value should count equally and no extreme values distort it; the median when skew or outliers would drag the mean away from the typical case; and the mode when the most common value is what matters, including categorical answers.
| Measure | Use it when | Example |
|---|---|---|
| Mean | Every value should count equally and there are no extreme outliers | Averaging test scores in a class |
| Median | Skewed data, where a few very large values would drag the mean away from the typical case | House prices or incomes |
| Mode | The most frequent value or category is the point | Most common shoe size sold, most common survey answer |
When the mean and median disagree noticeably, that disagreement itself is information: it tells you which way the data is skewed. For roughly symmetric, single-peaked data the three sit close together, and a common textbook approximation relates them: mode ≈ 3 × median − 2 × mean.
Skew, quartiles and outliers: reading the rest of the output
The table below the headline numbers answers the follow-up questions: how spread out is the data, where does the middle half sit, and is anything suspicious. Q1 and Q3 bound the middle 50 percent of the values, and the OpenStax quartiles and percentiles section shows why ordered data is the prerequisite for all of it.
The outlier rule is the standard one: anything below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is flagged, which is the construction the NIST box-plot page documents, and the OpenStax chapter review gives the same two fence expressions. Two points of honest disclosure matter here. First, other calculators use different quartile conventions: some interpolate percentiles, so their Q1/Q3 will differ slightly from the Tukey hinges used here. Neither is wrong; they are different conventions, and this page states its convention on the results panel. Second, the population standard deviation divides by n and the sample one by n − 1; the NIST measures of scale page discusses why the standard deviation is the right scale estimate when data look roughly normal, and the IQR when they do not.
Once you have the mean and standard deviation, two natural next steps are the coefficient of variation calculator, which expresses spread relative to the mean, and the area to z-score calculator, which turns a mean and standard deviation into probabilities. If quartiles sent you looking for percentiles, the blood pressure percentile calculator is the site’s percentile tool.
What competing calculators miss
Most mean-median-mode tools stop at the three headline numbers, and the ones that go further tend to hide their choices:
- Basics-only tools (GraphCalc and similar): mean, median, mode and a worked example or two. Fine for homework, but no quartiles, no standard deviation, no steps to audit.
- Step-by-step tutors (LearnMath): genuinely good guided working, but the walkthrough is mean-centric; median and mode live behind separate modes, and there is no spread statistics output.
- Full-stats tools (ShortCalc’s version): the strongest rival, with range, quartiles, both standard deviations and an outlier rule. The gap: its quartiles come from linear-interpolation percentiles rather than Tukey hinges, and it never states that, so its Q1/Q3 quietly differ from ours on the same data.
- Omni Calculator’s version: mean, median, mode, range and midrange with all steps plus Excel functions. Solid, but thin on spread: no quartiles, no IQR, no outlier flagging.
- Tutorial pages (StatisticsHowTo): thorough TI-83 walkthroughs, but a tutorial is not an interactive tool you can paste a spreadsheet column into.
- The gap this page fills: the three headline measures plus the full audit trail in one place, the sorted list, a frequency table, both standard deviations, Tukey-hinge quartiles stated on the panel, the 1.5 × IQR outlier check, a skew reading, and a count of any non-numeric entries that were skipped instead of silently zeroed.
Frequently asked questions
The mean is the sum of all values divided by how many there are. The median is the middle value of the sorted list, or the average of the two middle values when the count is even. The mode is the value that occurs most frequently. A data set can have all three be different numbers, and each describes the center in its own way.
Yes. If two or more values tie for the highest frequency, the data set is multimodal, and this calculator lists every tied value in ascending order. If every value appears exactly once, there is no mode at all.
Use the median when outliers or skew would distort the average. Incomes are the classic example: a handful of very high earners can drag the mean far above what a typical person earns, while the median stays representative. House prices work the same way.
This calculator uses Tukey hinges. The sorted data is split into a lower and an upper half; with an odd count the median value itself is excluded from both halves, and Q1 and Q3 are the medians of those halves. Other tools use percentile interpolation, which gives slightly different quartiles on the same data. Neither convention is wrong, but they are not interchangeable, so this page states its method on the results panel.
The population standard deviation divides the squared distances by n and describes the numbers you entered as a complete group. The sample standard deviation divides by n minus 1, which corrects for the fact that a sample underestimates the spread of the larger group it came from. Use the population figure when your data is the whole population and the sample figure when it is a sample.
The calculator compares the mean with the median. If the mean sits above the median, the data is right-skewed: a tail of high values is pulling the average up. If it sits below, the data is left-skewed. When they are essentially equal, the distribution reads as roughly symmetric.
Any value below Q1 minus 1.5 times the IQR, or above Q3 plus 1.5 times the IQR, is flagged as a possible outlier. These are the standard Tukey fences used in box plots. Flagged values are worth a second look, not automatic deletion.
Commas, spaces, tabs, semicolons, pipes and line breaks all work as separators, so a column copied from a spreadsheet pastes straight in. Decimals and negative numbers are fine. Anything that is not a number is skipped, and the results note tells you how many entries were ignored.
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References
- National Institute of Standards and Technology / SEMATECH. e-Handbook of Statistical Methods, 1.3.5.1: Measures of Location. Accessed October 23, 2026.
- OpenStax. Introductory Statistics 2e, 2.5: Measures of the Center of the Data. Accessed October 23, 2026.
- OpenStax. Introductory Statistics, 2.3: Measures of the Location of the Data. Accessed October 23, 2026.
- National Institute of Standards and Technology / SEMATECH. e-Handbook of Statistical Methods, 1.3.3.7: Box Plot. Accessed October 23, 2026.
- National Institute of Standards and Technology / SEMATECH. e-Handbook of Statistical Methods, 1.3.5.6: Measures of Scale. Accessed October 23, 2026.
- OpenStax. Introductory Statistics, Chapter 2 Review. Accessed October 23, 2026.