Quick answer
Descriptive statistics summarise data: for 1, 2, 3, 4, 5 the mean is 3, the count 5, the sum 15, the median 3, there is no mode, and the sample variance is 2.5 with a standard deviation of 1.5811.
Enter the data and choose sample or population. The calculator returns the mean, median, mode, variance, standard deviation and more.
Related tools: Standard Deviation Calculator: Sample or population standard deviation with variance and mean. Z-Score Calculator: Standardize a value using a mean and standard deviation. Mean Median Mode Range Calculator: Mean, median, mode and range of a data set.
How to use the Descriptive Statistics Calculator
- Type data set, for example 4, 8, 15, 16, 23, 42.
- Choose data type: Sample (n − 1) and Population (n).
- 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 | — |
| Data type | Choose one: Sample (n − 1); Population (n) | Starts at Sample (n − 1) |
Formula and method
Formula
See mean, median, mode, variance, standard deviation and quartile definitions
IEEE-754 double precision; shown to at most 6 decimal places.
Combines the individual calculators; quartiles use the inclusive linear-interpolation percentile.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Data set = 1, 2, 3, 4, 5; Data type = Sample (n − 1).
| Result | Value |
|---|---|
| Mean | 3 |
| Count | 5 |
| Sum | 15 |
| Median | 3 |
| Mode | None |
| Variance | 2.5 |
| Std. deviation | 1.581139 |
The first line is the headline result (mean). Below it the descriptive Statistics Calculator lists count, sum, median, mode, variance and std. deviation, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Sample or population
The sample variance divides by n − 1: 10 ÷ 4 = 2.5, giving s = 1.5811. A population variance divides by n: 10 ÷ 5 = 2. Choose according to whether your data are the whole group or a sample.
Beyond the mean
The mean is sensitive to outliers; the median is robust. Spread (standard deviation, quartiles) matters as much as the centre. Sample statistics need at least two values.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Data set: entering "1" shows "A sample needs at least two values." beside that field and no result.
Choosing between the Descriptive Statistics 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 |
|---|---|---|
| [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 |
| [Mean Median Mode Range Calculator](/statistics/mean-median-mode-range-calculator/) | data set | Mean |
| [Median Calculator](/statistics/median-calculator/) | data set | Median |
| [Relative Standard Deviation Calculator](/statistics/relative-standard-deviation-calculator/) | data set and data type | Relative standard deviation |
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
- Sample statistics need at least two values
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 mode of 1, 2, 3, 4, 5?
None, as no value repeats.
When to use median over mean?
With skewed data or outliers.
What is variance?
The average squared deviation.
What does the Descriptive Statistics Calculator calculate?
Count, mean, median, mode, spread, quartiles and range in one place. It returns Mean, Count, Sum, Median and Mode.
What formula does the Descriptive Statistics Calculator use?
See mean, median, mode, variance, standard deviation and quartile definitions. Combines the individual calculators; quartiles use the inclusive linear-interpolation percentile.
What do I need to enter in the descriptive Statistics Calculator?
You enter Data set and Data type.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Sample statistics need at least two values.
What does the “Data type” option change?
It sets how the descriptive Statistics is worked out. The choices are Sample (n − 1) and Population (n).
What is an example of a descriptive Statistics result?
With data set 1, 2, 3, 4, 5 and data type Sample (n − 1), the mean is 3.
Related calculators
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Z-Score Calculator — Standardize a value using a mean and standard deviation.
- Mean Median Mode Range Calculator — Mean, median, mode and range of a data set.
- Median Calculator — Median of a data set.
- Relative Standard Deviation Calculator — Relative standard deviation (RSD) as a percentage.
- Variance Calculator — Sample or population variance.
- Sum of Squares Calculator — Sum of squared deviations from the mean, and sum of squared values.
- Coefficient of Variation Calculator — Standard deviation relative to the mean.
- Midrange Calculator — Midpoint between the smallest and largest value.
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.