In probability and statistics, the variance of a random variable is the average value of the square distance from the mean value. It represents the how the random variable is distributed near the mean value. Small variance indicates that the random variable is distributed near the mean value. Big variance indicates that the random variable is distributed far from the mean value. For example, with normal distribution, narrow bell curve will have small variance and wide bell curve will have big variance.
The variance of random variable X is the expected value of squares of difference of X and the expected value μ.
σ2 = Var ( X ) = E [(X - μ)2]
From the definition of the variance we can get
σ2 = Var ( X ) = E(X 2) - μ2
Variance of continuous random variable
For continuous random variable with mean value μ and probability density function f(x):
Variance of discrete random variable
For discrete random variable X with mean value μ and probability mass function P(x):
Properties of variance
When X and Y are independent random variables:
Var(X+Y) = Var(X) + Var(Y)
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
- Online Tools
- Text Tools
- PDF Tools
- Probability & Statistics
- Calculus & analysis
- Mathematical symbols
- Basic probability
- Expectation (E)
- Variance (Var)
- Standard deviation (std)
- Probability distribution
- Normal distribution
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.