Mean, median and mode: the three measures of center
The mean, the median and the mode are the three most common ways to summarize a set of numbers with a single “typical” value. Each answers a different question, and when the data are skewed they can land far apart. This calculator gives you all three at once, along with the range, sum, count and standard deviation, so you see the full shape of your data in one place.
Everything runs in your browser — you paste the numbers and nothing is sent to any server.
How to use the calculator
- Paste or type your numbers into the text box. Separate them with a comma, a space or a line break; the tool ignores the separators and drops anything that is not a number.
- Results appear instantly: mean, median and mode on the dark card, and below it the count, sum, range, minimum and maximum, and both the population and sample standard deviation.
- Use Copy summary to grab every result as text, or Clear to start over.
There is no “calculate” button — everything recomputes as soon as you change the text.
The formulas
- Mean (average): the sum of all values divided by how many there are. Mean = Σx / n.
- Median: the middle value once the data are sorted from smallest to largest. With an odd count it is the middle one; with an even count it is the average of the two central values.
- Mode: the value (or values) that occurs most often. There can be several modes (multimodal) or none if every value appears exactly once.
- Range: maximum minus minimum.
- Standard deviation: measures how spread out the data are around the mean. The population version divides by
n; the sample version divides byn − 1(Bessel’s correction) and is used when your data are a sample drawn from a larger group.
| Measure | What it represents | Sensitive to extreme values |
|---|---|---|
| Mean | Numerical balance point | Yes, strongly |
| Median | Central value by position | No |
| Mode | Most frequent value | No |
Worked example
Take the set 2, 4, 4, 4, 5, 5, 7, 9 (8 values).
- Sum: 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9 = 40
- Mean: 40 / 8 = 5
- Median: they are already sorted; with 8 values (even) it is the average of the 4th and 5th: (4 + 5) / 2 = 4.5
- Mode: the 4 appears 3 times, more than any other value, so the mode is 4
- Range: 9 − 2 = 7
- Population standard deviation: the squared differences from the mean (5) add up to 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32; the variance is 32 / 8 = 4, and its square root is 2
- Sample standard deviation: variance 32 / 7 ≈ 4.571, whose square root is ≈ 2.14
Notice the mean (5) and the median (4.5) don’t match: the high value (9) pulls the mean up, while the median doesn’t budge.
Frequently asked questions
When is the median better than the mean?
When there are extreme values or the distribution is skewed. With salaries, for example, a few very high pay packets inflate the mean, so the median better describes what a “typical” person earns. The mean is ideal when the data are fairly symmetric and free of outliers.
Can a data set have no mode?
Yes. If every number appears exactly once, there is no mode because none stands out by frequency. There can also be two or more modes (bimodal or multimodal) when several values tie for the highest frequency; the calculator lists them all.
What’s the difference between population and sample standard deviation?
The population version divides by n and is used when your data are the entire population you care about. The sample version divides by n − 1 and is used when the data are a sample from which you want to estimate the variability of the whole group; that adjustment corrects the bias and yields a slightly larger value.
Which separators can I use when pasting numbers?
Comma, space or line break, in any mix. You can paste a column from a spreadsheet or a comma-separated list and it works either way. Any chunk that isn’t a valid number is discarded without an error.
Does it handle decimals and negative numbers?
Yes. Use a dot as the decimal separator (for example 2.5) and a minus sign for negatives (-3). The calculator sorts and processes them just like positive integers.