Mean, Median & Mode Calculator
It computes the full set of descriptive statistics for any list of numbers: mean, median, mode, range, variance and standard deviation.
Mean (average)
5.0000
Mean
5.0000
Median
4.5000
Mode
4.00
Count
8
Sum
40.00
Range
7.00
Minimum
2.00
Maximum
9.00
Sample SD (s)
2.1381
Population SD (σ)
2.0000
Sample variance
4.5714
Population variance
4.0000
Sorted
2.00, 4.00, 4.00, 4.00, 5.00, 5.00, 7.00, 9.00
What it calculates
It computes the full set of descriptive statistics for any list of numbers: mean, median, mode, range, variance and standard deviation.
Why it matters
The mean alone hides the shape of data. One outlier can drag it far from the typical value, which is exactly when the median and standard deviation matter.
Who it's for
Students, researchers, analysts and anyone summarizing a set of measurements or test scores.
Formula
- x̄
- Mean — the arithmetic average
- σ
- Population standard deviation (divides by n)
- s
- Sample standard deviation (divides by n − 1)
- n
- Number of values
Worked example
2, 4, 4, 4, 5, 5, 7, 9
- 1Mean = 40 ÷ 8 = 5
- 2Squared deviations sum to 32
- 3Population variance = 32 ÷ 8 = 4
- 4σ = √4
Mean 5, median 4.5, mode 4, population SD exactly 2
How the mean, median & mode calculator works
The mean is the sum over the count. The median is the middle value once sorted, or the average of the two middle values for an even count. The mode is whichever value occurs most often — and if nothing repeats, there is no mode. Standard deviation is the square root of the average squared distance from the mean; dividing by n − 1 instead of n corrects the bias when your numbers are a sample rather than the whole population.
The mean is the sum over the count, the median is the middle value once sorted, and the mode is whichever value occurs most often. If nothing repeats there is no mode at all.
Standard deviation is the square root of the average squared distance from the mean. Dividing by n − 1 rather than n corrects the bias when your numbers are a sample rather than the entire population — use the sample figure unless you measured everyone.
Common mistakes
- Using population standard deviation on sample data, which understates the spread.
- Reporting a mode when every value appears exactly once — there is none.
- Quoting a mean for skewed data where the median describes the typical case far better.
Tips and best practice
- If mean and median differ noticeably, the data is skewed and the median is the honest summary.
- Use the sample formula unless you genuinely measured every member of the group.
Frequently asked questions
What is the difference between sample and population standard deviation?
Population divides the squared deviations by n; sample divides by n − 1. The sample version is slightly larger and corrects the bias from estimating the mean from the same data.
When should I use the median instead of the mean?
When the data is skewed or contains outliers. Incomes are the classic case: a few very high values pull the mean well above the typical earner.
Can a data set have more than one mode?
Yes. If two or more values tie for the highest frequency, the set is bimodal or multimodal and every tied value is a mode.
What does standard deviation actually tell me?
The typical distance of a value from the mean. Roughly two thirds of values in a normal distribution fall within one standard deviation of the mean.
How do I enter my numbers?
Paste them separated by commas, spaces or new lines. Anything that is not a number is ignored.
Related calculators
Methodology & trust
- Formula source
- Standard descriptive statistics; Bessel's correction for the sample variance.
- Last updated
- 2026-07-28
- Privacy
- Every calculation runs in your browser. No inputs are sent to a server or stored.
- Accessibility
- Keyboard navigable, labeled inputs and WCAG AA color contrast.