standarddeviationcalculator.net

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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

Which calculator do I need?

You have or wantUse
A list of numbers and you want how spread out they areStandard deviation calculator
A list of numbers and you want the typical valueMean, median, mode & range
Every summary figure at once: mean, SD, quartiles, skewnessDescriptive statistics calculator
Where one value sits relative to the restZ-score calculator
A picture of how the values are distributedHistogram maker
Whether two groups really differT-test calculator
Whether two variables move togetherCorrelation coefficient
A range that probably contains the true meanConfidence interval calculator

Describe a dataset

The calculators people reach for first: centre, spread and position of a single list of numbers.

Estimate and test

For going beyond the sample: how precise a mean is, whether a difference is real and how variables relate.

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:

QuestionMeasureResult
Typical valueMean5
Middle valueMedian4.5
Most common valueMode4
Spread, treating the 8 as the whole populationPopulation SD (σ)2
Spread, treating the 8 as a sampleSample SD (s)2.138
Precision of the meanStandard error s/√n0.756

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

Common questions

Which statistics calculator should I start with?
If you have a single list of numbers, start with the descriptive statistics calculator: it gives the mean, median, standard deviation, quartiles and skewness together. From there, open the calculator for the one figure you need to explain or report in detail.
What is the difference between descriptive and inferential statistics?
Descriptive statistics summarise the data you actually have, such as its mean and spread. Inferential statistics use a sample to draw conclusions about a larger population, with confidence intervals, standard errors and hypothesis tests that allow for sampling error.
Do these calculators store or upload my data?
No. The calculations run in your browser, so the numbers you paste are not sent to a server. You can use them with confidential or unpublished data.