Statistics calculators
Every statistics calculator on the site, sorted into ten categories: describing a dataset (standard deviation, averages, spread, quartiles, charts) and drawing conclusions from it (correlation, tests, sampling, error, index numbers). Each tool shows its working, so students can check homework and analysts can check a figure before it goes in a report.
Statistics categories
-
Standard deviation
Standard deviation and variance calculators for lists, frequency tables, weighted and pooled groups, CSV files and large datasets, with the working shown. 28 calculators.
-
Averages
Calculators for the mean, median and mode, plus weighted, geometric and harmonic means, midrange, RMS, grade and rating averages, each with worked steps. 19 calculators.
-
Spread and shape
Measures of spread and shape: range, mean and median absolute deviation, coefficient of variation, skewness, outliers and fences, and process capability. 19 calculators.
-
Quartiles and percentiles
Quartile, decile and percentile calculators for lists and grouped data: IQR, five-number summary, percentile rank and quartile and decile deviation. 10 calculators.
-
Charts and graphs
Make histograms, box plots, dot plots, stem-and-leaf plots, pie charts, scatter plots and frequency tables from your own data, with the numbers behind each. 16 calculators.
-
Correlation & regression
Pearson, Spearman and Kendall correlation, covariance, R², and linear, multiple, logistic and curve regression, each with the working and a scatter plot. 17 calculators.
-
Hypothesis tests
T-tests, z-tests, ANOVA, chi-square, Fisher, McNemar and rank tests, plus p-values, critical values, effect sizes and power, all with the working shown. 20 calculators.
-
Sampling & estimation
Sample size, margin of error, confidence intervals, standard error, the central limit theorem and sampling distributions, plus control limits and Benford tests. 18 calculators.
-
Error & uncertainty
Error propagation, measurement uncertainty, relative and percent error, RSE, MSE and residuals, plus raw scores and Shannon and Simpson diversity indices. 12 calculators.
-
Index numbers
Laspeyres, Paasche, Fisher, Marshall–Edgeworth, Dorbish–Bowley and Kelly price indices, plus simple aggregative and price relative methods, with the tables. 11 calculators.
Which calculator do I need?
| You have or want | Use |
|---|---|
| A list of numbers and you want how spread out they are | Standard deviation calculator |
| A list of numbers and you want the typical value | Mean, median, mode & range |
| Every summary figure at once: mean, SD, quartiles, skewness | Descriptive statistics calculator |
| Where one value sits relative to the rest | Z-score calculator |
| A picture of how the values are distributed | Histogram maker |
| Whether two groups really differ | T-test calculator |
| Whether two variables move together | Correlation coefficient |
| A range that probably contains the true mean | Confidence interval calculator |
Describe a dataset
The calculators people reach for first: centre, spread and position of a single list of numbers.
-
Standard deviation calculator
Sample and population standard deviation of a list, with every step of the working.
-
Variance calculator
Sample and population variance, the sum of squares, and the conversion to and from SD.
-
Mean, median, mode & range
The mean, median, mode and range of a list in one pass.
-
Descriptive statistics calculator
A full summary table: count, mean, SD, quartiles, skewness and kurtosis.
-
Percentile calculator
The value at any percentile of your data, or the percentile rank of a value.
-
Z-score calculator
How many standard deviations a value sits from the mean, with its percentile.
Estimate and test
For going beyond the sample: how precise a mean is, whether a difference is real and how variables relate.
-
Standard error calculator
The standard error of the mean from raw data, or the SD behind a published SE.
-
Confidence interval calculator
A t-based confidence interval for a mean from x̄, s and n, with the margin of error.
-
T-test calculator
One-sample, paired and two-sample t-tests with the p-value and effect size.
-
Correlation coefficient
Pearson's r and Spearman's rho for paired data, with a significance test.
-
Linear regression calculator
The least-squares line with slope, intercept, R², a significance test and a scatter plot.
-
Sample size calculator
How many responses you need for a given margin of error and confidence.
How the statistics calculators fit together
Most statistics work runs in the same order. First you describe the data you have: a typical value (the mean or median), how far values stray from it (the standard deviation, range or IQR) and what the distribution looks like (a histogram or box plot). Then, if the data are a sample from something larger, you infer: how precise the sample mean is (standard error, confidence interval) and whether a pattern could be chance (t-test, chi-square, p-value).
The first five categories above cover description; the last five cover inference, relationships between variables, measurement error and index numbers.
One dataset, several answers
Take the eight values 2, 4, 4, 4, 5, 5, 7, 9. Each calculator answers a different question about them:
| Question | Measure | Result |
|---|---|---|
| Typical value | Mean | 5 |
| Middle value | Median | 4.5 |
| Most common value | Mode | 4 |
| Spread, treating the 8 as the whole population | Population SD (σ) | 2 |
| Spread, treating the 8 as a sample | Sample SD (s) | 2.138 |
| Precision of the mean | Standard error s/√n | 0.756 |
The two standard deviations differ only in the divisor: 32/8 = 4 for the population variance, 32/7 ≈ 4.571 for the sample variance. Use the sample version whenever the numbers are a sample and you want to say something about the wider group, which is most of the time.
Common mix-ups
- Standard deviation vs standard error. The SD describes the spread of individual values; the SE describes how much the mean itself would vary between samples. The SE shrinks as n grows; the SD does not.
- Mean vs median. One large value drags the mean but barely moves the median, so report the median for skewed data such as incomes or house prices.
- Correlation vs regression. Correlation gives one number for the strength of a linear link; regression gives the line itself so you can predict y from x.
Guides to read alongside
-
Standard deviation examples
Ten real-world problems worked in full, from exam scores to stock returns.