Paste a list of numbers to see the mean, median, standard deviation, quartiles and shape of your data at once
This statistics calculator summarizes numeric data such as test scores, sales figures or measurements. The mean and median show the center, the standard deviation and interquartile range show the spread, skewness and kurtosis describe the shape, and a histogram with a box plot shows the same picture visually.
So that you can compare results with a spreadsheet, it uses the same formulas as Excel for sample and population variance (STDEV.S, STDEV.P), quartile methods (QUARTILE.INC, QUARTILE.EXC), and skewness and kurtosis (SKEW, KURT). The confidence interval for the mean does not use a rough 1.96; it uses the t value that matches your degrees of freedom.
How to use the calculator
- Paste your data: separate numbers with commas, spaces or new lines. You can copy a whole spreadsheet column as it is. Anything that is not a number is left out, and the calculator tells you what it skipped.
- Choose sample or population: pick sample (n−1) if your data is a subset drawn from a larger group, and population (n) if it covers every member you care about. Most data is a sample.
- Read the results: the mean and key figures appear first, followed by the distribution chart, quartiles, outliers, skewness and kurtosis. The frequency table and per-value Z-scores can be expanded.
Sample vs. population: what changes
| Measure | Sample | Population | Excel function |
|---|---|---|---|
| Variance | Σ(x − x̄)² ÷ (n − 1) | Σ(x − μ)² ÷ n | VAR.S / VAR.P |
| Standard deviation | √ sample variance | √ population variance | STDEV.S / STDEV.P |
| Skewness | n ÷ ((n−1)(n−2)) × Σz³ | (1/n) × Σz³ | SKEW / SKEW.P |
| Confidence interval for the mean | x̄ ± t × s ÷ √n | Not applicable | CONFIDENCE.T |
A sample estimates its mean from the data itself, so dividing the sum of squared deviations by n would understate the variance. Dividing by n − 1 corrects that bias. With 30 values, the sample variance is 30/29 times the population variance.
Example: 30 test scores
These are the results for the built-in "Even spread" sample (scores from 58 to 82, 30 students).
| Measure | Result |
|---|---|
| Mean / median | 70.8 / 71 |
| Mode | 70, 71 (3 times each) |
| Standard deviation (sample / population) | 5.4101 / 5.3191 |
| Q1 / Q3 / IQR (INC) | 68 / 74 / 6 |
| Outlier fences | below 59 or above 83 → 58 |
| Skewness / kurtosis | −0.1737 / 0.1187 |
| 95% confidence interval for the mean (t = 2.0452) | 68.7798 to 72.8202 |
The mean and median are almost equal and the skewness is close to 0, so the data is nearly symmetric. The single score of 58 is flagged as an outlier by the 1.5×IQR rule, but that flag only means "this value sits apart from the rest, so take a look"; it does not mean the value is wrong.
Why quartiles differ between programs
There are several ways to interpolate between sorted values to get a quartile. Excel's QUARTILE.INC and R's default (type 7) place the position at (n − 1) × p, while Excel's QUARTILE.EXC and the NIST handbook use (n + 1) × p. For the 11 values 1 to 11, Q1 is 3.5 with the INC method and 3 with the EXC method. The EXC method cannot be computed when there are too few values (Excel returns #NUM!), and the calculator shows the same "cannot be calculated" state. When you need to match another program, check which method it uses first.
The t values behind the confidence interval
| Degrees of freedom (n − 1) | 90% | 95% | 99% |
|---|---|---|---|
| 4 | 2.132 | 2.776 | 4.604 |
| 9 | 1.833 | 2.262 | 3.250 |
| 19 | 1.729 | 2.093 | 2.861 |
| 29 | 1.699 | 2.045 | 2.756 |
| 99 | 1.660 | 1.984 | 2.626 |
With 5 values (4 degrees of freedom), a 95% interval needs the multiplier 2.776. Using the normal-distribution value 1.96 instead would make the interval almost 30% too narrow. Rough shortcuts such as applying a flat 2.05 to every sample under 30 also understate the interval for small samples. A 95% confidence interval does not mean there is a 95% probability that the true mean lies inside it; it means that if you built intervals the same way many times, about 95% of them would contain the true mean.
How to read skewness and kurtosis
- Skewness: 0 means symmetric, a positive value means a longer right tail (large values), and a negative value means a longer left tail. For right-skewed data such as income, the median represents a typical value better than the mean.
- Kurtosis: this is excess kurtosis, as in Excel's KURT, where the normal distribution is 0. A positive value means heavier tails than normal (extreme values are more common) and a negative value means lighter tails.
- Skewness needs at least 3 values and kurtosis at least 4. With few values both swing widely, so read them together with the chart.
Common mistakes
- Using the population formula on sample data: if you surveyed only part of the group, dividing by n understates the spread.
- Looking only at the mean of skewed data: a single outlier can move the mean a lot. The "With outliers" sample has a mean of 17.5 and a median of 15.
- Deleting outliers right away: the 1.5×IQR rule only points out values worth checking. Find out whether it is a typo or a real measurement first.
- Using the mode on continuous data: measurements that differ in the decimals rarely repeat, so the mode says little. Look at the tallest bin in the frequency table instead.
Limitations
- It calculates descriptive statistics for one variable only. It does not do correlation or regression between two variables, hypothesis tests (such as a t-test) or normality tests.
- The confidence interval assumes a random sample and a sampling distribution of the mean that is close to normal. It is unreliable with few values and strong skew.
- The geometric and harmonic means are shown only when every value is greater than 0.
- Your data is calculated on this page only and is not stored in the address bar or in any storage.
Reference date Sources were checked on 2026-10-09, and the table values were calculated with this calculator.
Sources
- 01NIST/SEMATECH e-Handbook: Critical Values of the Student's t Distributiont critical values by degrees of freedom (95% two-sided: 2.776 at 4, 2.262 at 9, 2.045 at 29)
- 02NIST/SEMATECH e-Handbook: Confidence Limits for the MeanWhat a 95% confidence interval means (not a 95% chance that the true mean is inside)
- 03NIST/SEMATECH e-Handbook: Box Plot1.5 times the interquartile range for fences and whiskers
- 04Microsoft Support: QUARTILE.EXC · QUARTILE.INCQuartiles based on inclusive and exclusive 0..1 percentiles
- 05Microsoft Support: SKEW · KURTSample skewness (3 or more values) and excess kurtosis (4 or more)
- 06R stats::quantile documentationNine methods from Hyndman & Fan (1996), default type 7
Frequently asked questions
How do sample and population standard deviation differ?
A sample divides the sum of squared deviations by n − 1, a population by n. Use the sample version (Excel STDEV.S) when your data is a subset of a larger group, and the population version (STDEV.P) when it covers every member. For the 30 example scores, the sample value is 5.4101 and the population value is 5.3191.
Should I look at the mean or the median?
If the data is symmetric, they are close and the mean works well. When a few large values pull the mean upward, as with income, the median is a better typical value. In the calculator's "With outliers" sample, the mean is 17.5 and the median is 15.
Why do my quartiles differ from Excel?
Quartiles can be calculated in several ways. Excel QUARTILE.INC and R's default use position (n − 1) × p, while QUARTILE.EXC uses (n + 1) × p. For 1 to 11, Q1 is 3.5 with INC and 3 with EXC. Choose the same method in the calculator and you get Excel's values.
How are outliers decided?
A value is flagged if it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR (Tukey's box plot rule). In the example scores the fences are 59 and 83, so the score of 58 is flagged. An outlier is a value worth checking, not necessarily a wrong one.
What does a confidence interval mean?
If you drew samples and built intervals the same way many times, about 95% of them would contain the true mean. It is wrong to say there is a 95% chance the true mean lies in one particular interval. The calculator uses mean ± t × standard error, and the 95% interval for the 30 example scores is 68.7798 to 72.8202.
Why use a t value instead of 1.96?
When the population standard deviation is unknown and estimated from the sample, the t distribution applies. With 5 values the 95% t value is 2.776, so using 1.96 would make the interval almost 30% too narrow. As the sample grows, t approaches 1.96 (1.984 at 99 degrees of freedom).
How do I read skewness and kurtosis?
Skewness of 0 means symmetric, positive means a longer right tail and negative means a longer left tail. Kurtosis is excess kurtosis with the normal distribution at 0; a positive value means heavy tails with frequent extreme values. The formulas match Excel's SKEW and KURT, so the values agree.
Can I paste data copied from Excel?
Yes. A pasted column is read as numbers separated by new lines. You can also separate values with commas or spaces. Non-numeric text such as headers is skipped, and the calculator tells you what it left out. Your data is calculated on this page only.