Standard deviation (σ) calculator with mean value & variance online.

## Population and sampled standard deviation calculator

Enter data values delimited with commas (e.g: 3,2,9,4) or spaces (e.g: 3 2 9 4) and press the *Calculate* button.

## Discrete random variable standard deviation calculator

Enter probability or weight and data number in each row:

## Whole population standard deviation calculation

Population mean:

Population standard deviation:

## Sampled data standard deviation calculation

Sample mean:

Sample standard deviation:

## Discrete random variable standard deviation calculation

Random variable mean:

Discrete random variable standard deviation:

## What is standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.[1] A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter sigma σ, for the population standard deviation, or the Latin letter s, for the sample standard deviation.[2]

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.[3][4] A useful property of the standard deviation is that unlike the variance, it is expressed in the same unit as the data.

The standard deviation of a population or sample and the standard error of a statistic (e.g., of the sample mean) are quite different, but related. The sample mean's standard error is the standard deviation of the set of means that would be found by drawing an infinite number of repeated samples from the population and computing a mean for each sample. The mean's standard error turns out to equal the population standard deviation divided by the square root of the sample size, and is estimated by using the sample standard deviation divided by the square root of the sample size. For example, a poll's standard error (what is reported as the margin of error of the poll), is the expected standard deviation of the estimated mean if the same poll were to be conducted multiple times. Thus, the standard error estimates the standard deviation of an estimate, which itself measures how much the estimate depends on the particular sample that was taken from the population.

In science, it is common to report both the standard deviation of the data (as a summary statistic) and the standard error of the estimate (as a measure of potential error in the findings). By convention, only effects more than two standard errors away from a null expectation are considered "statistically significant", a safeguard against spurious conclusion that are really due to random sampling error.

When only a sample of data from a population is available, the term standard deviation of the sample or sample standard deviation can refer to either the above-mentioned quantity as applied to those data, or to a modified quantity that is an unbiased estimate of the population standard deviation (the standard deviation of the entire population).

- Bland, J.M.; Altman, D.G. (1996). "Statistics notes: measurement error". BMJ. 312 (7047): 1654. doi:10.1136/bmj.312.7047.1654. PMC 2351401. PMID 8664723.
- "List of Probability and Statistics Symbols". Math Vault. 26 April 2020. Retrieved 21 August 2020.
- Gauss, Carl Friedrich (1816). "Bestimmung der Genauigkeit der Beobachtungen". Zeitschrift für Astronomie und Verwandte Wissenschaften. 1: 187–197.
- Walker, Helen (1931). Studies in the History of the Statistical Method. Baltimore, MD: Williams & Wilkins Co. pp. 24–25.

Currently, we have around 945 calculators, conversion tables and usefull online tools and software features for students, teaching and teachers, designers and simply for everyone.

You can find at this page financial calculators, mortgage calculators, calculators for loans, calculators for auto loan and lease calculators, interest calculators, payment calculators, retirement calculators, amortization calculators, investment calculators, inflation calculators, finance calculators, income tax calculators, compound interest calculators, salary calculator, interest rate calculator, sales tax calculator, fitness & health calculators, bmi calculator, calorie calculators, body fat calculator, bmr calculator, ideal weight calculator, pace calculator, pregnancy calculator, pregnancy conception calculator, due date calculator, math calculators, scientific calculator, fraction calculator, percentage calculators, random number generator, triangle calculator, standard deviation calculator, other calculators, age calculator, date calculator, time calculator, hours calculator, gpa calculator, grade calculator, concrete calculator, subnet calculator, password generator conversion calculator and many other tools and for text editing and formating, downloading videos from Facebok (we built one of the most famous Facebook video downloader online tools). We also provide you online downloanders for YouTube, Linkedin, Instagram, Twitter, Snapchat, TikTok and other social media sites (please note we does not host any videos on its servers. All videos that you download are downloaded from Facebook's, YouTube's, Linkedin's, Instagram's, Twitter's, Snapchat's, TikTok's CDNs. We also specialise on keyboard shortcuts, ALT codes for Mac, Windows and Linux and other usefull hints and tools (how to write emoji online etc.)

There are many very usefull online free tools and we would be happy if you share our page to others or send us any suggestions for other tools which will come on your mind. Also in case you find any of our tools that it does not work properly or need a better translation - please let us know. Our tools will make your life easier or simply help you to do your work or duties faster and in more effective way.

These below are the most commonly used by many users all over the world.

- Free online calculators and tools
- Free online units conversion tools
- Free online web design tools
- Free online electricity & electronics tools
- Mathematics
- Online Tools
- Text Tools
- PDF Tools
- Code
- Ecology
- Others
- Free online electrical calculators and tools
- Free online financial calculators and tools
- Free online grade calculators and tools
- Free online lighting calculators and tools
- Free online math calculators and tools
- Free online wire calculators and tools
- Free online time calculators and tools
- Free online baby calculators and tools
- Free online body calculators and tools
- Math free online calculator
- Adding fractions free online calculator
- Addition free online calculator
- Antilog free online calculator
- Arccos free online calculator
- Arcsin free online calculator
- Arctan free online calculator
- Average free online calculator
- Base free online calculator
- Binary free online calculator
- Convolution free online calculator
- Cosine free online calculator
- Dividing fractions free online calculator
- Division free online calculator
- Exponential growth/decay formula calculator online free
- Exponents free online calculator
- Factorial free online calculator
- Fractions free online calculator
- Greatest common factor free online calculator
- Least common multiple free online calculator
- Natural logarithm free online calculator
- Logarithm free online calculator
- Multiplication free online calculator
- Multiplying fractions free online calculator
- Percentage free online calculator
- Percentage change free online calculator
- Percent error free online calculator
- Percentage increase/decrease free online calculator
- Pythagorean theorem free online calculator
- Quadratic equation free online calculator
- Random number free online generator
- Ratio free online calculator
- Radicals and roots free online calculator
- Scientific notation free online calculator
- Simplifying fractions free online calculator
- Sine free online calculator
- Square root free online calculator
- Standard deviation free online calculator
- Subtracting fractions free online calculator
- Subtraction free online calculator
- Tangent free online calculator
- Trigonometry free online calculator
- Weighted average free online calculator
- Variance free online calculator
- Random number generator 1-2
- Random number generator 1-3
- Random number generator 1-4
- Random number generator 1-5
- Random number generator 1-6
- Random number generator 1-10
- Random number generator 1-20
- Random number generator 1-100
- Random number generator 0-1
- Random number generator 0-9
- Random number generator 0-10
- Random number generator 0-99
- Random number generator 0-100

And we are still developing more. Our goal is to become the one-stop, go-to site for people who need to make quick calculations or who need to find quick answer for basic conversions.

Additionally, we believe the internet should be a source of free information. Therefore, all of our tools and services are completely free, with no registration required. We coded and developed each calculator individually and put each one through strict, comprehensive testing. However, please inform us if you notice even the slightest error – your input is extremely valuable to us. While most calculators on Justfreetools.com are designed to be universally applicable for worldwide usage, some are for specific countries only.