What is Variance: Definition and 356 Discussions

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. In other words, it measures how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by




σ

2




{\displaystyle \sigma ^{2}}
,




s

2




{\displaystyle s^{2}}
, or



Var
⁡
(
X
)


{\displaystyle \operatorname {Var} (X)}
.

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  1. A

    Variance of the position noise

    Hi, I read an article in Kalman filtering. There is an example in introductory Mechanics. I just can not understand which formula for calculating the variance and covariance is used. The example is about a vehicle that is traveling straight on the road: The postition is measured with an...
  2. S

    MATLAB Allan variance implementation in matlab

    Hi everyone, Anyone out here who knows how to use MATLAB to generate rate random walk, angle random walk and flicker noise and to c wat is the allan variance plot like. Need the code to implement allan variance plot in particular. Thank you
  3. S

    How can I calculate the error in a slope with variance in x and y values?

    I am looking for methods to calculate the error in a slope. the caveat is that my values themselves are averages with a STDEV. E.g. x 1+-1% 2+-1% 3+-1% y 0.14+-0.01 0.27+-0.02 0.42+-0.02 (using...
  4. A

    Calculating the variance with a TWIST

    Calculating the variance with a TWIST! Hello! I am trying to understand this problem! its just on my practice questions and Ihave the answer, I CAN NOT understand how to set it up! PLEASE someon ehelpo! THis is it :) A student wants to calculate the variance of a set of 10 scores. But he...
  5. S

    Weighted verage of two variables with minimal variance

    Homework Statement X1 and X2 are independent random variables. They both have the same mean (mue). Their variances are s1^2 and s2^2 respectively, where s1^2 and s2^2 are known constants. It is proposed to estimate mue by an estimator T of the form T=c1X1 + c2X2. Show that T will be...
  6. V

    Variance of Variances and Space

    I think I'll ask it this way. Here goes... 1 point = zero dimensions. 2 points = 1, which is line; 3 points, shape; 4 minimum to have volume. Somewhere, or rather, when, time applies, most preferably at that case in which dimensionality, quite plainly, is. My question follows a...
  7. K

    Find the mean, variance, and standard deviation

    Homework Statement If there are 4 children in a family, find the probability of getting exactly 3 girls. Find the mean, variance, and standard deviation. Use two different methods(binomial distribution method and general probability distribution method). Homework Equations Binomial...
  8. M

    Finding variance without knowing mean?

    Hi, my girlfriend is taking a business statistics class and she had a test today. she got stumped on a question and wrote it down so she could ask me about it when she got back since I'm pretty good at math. I tried solving it but from what i can tell it seems like you would need to know the...
  9. M

    Finding variance without knowing mean?

    Hi, my girlfriend is taking a business statistics class and she had a test today. she got stumped on a question and wrote it down so she could ask me about it when she got back since I'm pretty good at math. I tried solving it but from what i can tell it seems like you would need to know...
  10. L

    Bayesian Inference for Determining Data and Noise Variance in Image Denoising

    Hello, I am working do determine an optimum threshold for wavelt transform image denoise. I have the following quesstion. considering a vector of a data d*: d*= d + noise where the noise is zero mean and with variance sigma ~(0,sigma) and the signal "d" has variance...
  11. M

    What is the variance of X/Y? Does it exist?

    I know Var(aX + bY)... I know Var(XY)... I don't know of a solution to Var(X/Y)... is there one?
  12. T

    How Do You Rearrange R Values for a Linear Graph in Inverse Proportion Problems?

    Homework Statement The data below: I(A): 6 12 18 24 F(R): 240 120 80 60 Rearrange the values of R so that a straight line graph will result. Homework Equations I have to find a proportional equation for I and F. Something like I = F The Attempt at...
  13. A

    Normal Distribution: Sample Mean & Variance

    ok guys , i need an answer to this question , use both moment generating function and cummulative function to show that z=(x(bar)-\mu)/(\sigma/\sqrt{n}) if x(bar) is based on a random sample of size n from a normal(\mu,\sigma^2)
  14. H

    I have variance of response. How can I find it's MSE?

    To All, I did a study and my response is defined as y = b1x1 + b2x2 + e where e ~N(0,1). I have y~N(4,33). In my data results, I did an ordinary least squares regression model for y = b1x1+b2x2+ e. The ANOVA is telling me the mean of y is 4, but MSE is 1. So here is my question. If I...
  15. S

    Intuitively, shouldn't variance always be 0?

    Ok I know that Var[X] = E[(X-E[X])^2]. But I just can't help but think that the variance should always be zero. I think it makes so much sense, but obviously the formula says otherwise... But look, my reasoning seems so perfect: 1) The variance is the expected difference from the mean...
  16. C

    Variance of resistance with significant current flow

    The value of a real-world resistor ( ) changes with significant time as the resistor conducts a current. Answer choices Never Rarely Sometimes Usually Always Explain why.
  17. K

    Find the variance of f(x) = 1/4 for -2<x<2

    find the variance for f(x)= 1/4 for -2<x<2 & 0 elsewhere The first thing I did was find the expected value, which was 1 (just integrated the original function from -2 to 2). Then I set up the next part as \int (x-1)^2 (1/4) dx with the limits -2 to 2 So it became 1/4\int x^2-2x+1 dx...
  18. C

    Stats - Geometric Variance Proof

    Stats -- Geometric Variance Proof Hi, I'm a student in South-East Indiana, enrolled in a AP Stats class. Our teacher has asked us to prove the geometric variance equation (the first equation pictured) USING ALGEBRA ONLY. I've gotten it all the way down to the 2nd equation and now I'm stuck...
  19. J

    Sample Variance: Why Divide by n-1?

    If I have a sample consisting of n measurements why is the sample variance the result of dividing by n-1 instead of n? jf
  20. H

    SAS: Calculating Variance of 3 Variables in Homework Statement

    Homework Statement Howdy I got a datasheet in the SAS data system with 3 variables and 60 obs. How do I most simply get SAS to calculate the variance? Homework Equations The Attempt at a Solution data cnn; input vara varb snt@@; datalines; ... ... ... run; proc...
  21. S

    Sample mean and sample variance

    Homework Statement The sample mean and sample variance of five data values are, respectively, 104 and 4. If three of the data values are 102 100 and 105, what are the other two values?The attempt at a solution My idea was to get two equations for the two unknowns, let's call them x and y. The...
  22. M

    Level of significans and confidens interval of the mean and the variance

    Homework Statement I am given the table \begin{array}{ccccc} samplesite & 1950 & 1975 & Change \\ 1 & 7.30 & 7.70 & 0.40\\ 2 & 6.14 & 6.72 & 0.58 \\ 3 & 6.47 & 6.32 & -0.15 \\4 & 5.87 & 6.38 & 0.51 \\ 5 & 6.06 & 6.34 & 0.28 \\ 6 & 4.71 & 5.78 & 1.07 \\ 7 & 5.45 & 5.59 & 0.14 \\ 8 & 6.17 &...
  23. B

    How Do You Calculate E(Y) and Var(Y) for Independent Random Variables?

    Homework Statement Say X has a density f(x) = 3x^(-4) if x > 1, and 0 otherwise. Now say X1,...,X16 are independent with density f. Let Y = (X1X2...X16)^(1/16). Find E(Y) and Var(Y). Homework Equations Var(Z) = E(Z^2) - [E(Z)]^2 E(Z) = Integral from -inf to +inf of z*f(z)dz The...
  24. C

    Conditional expectation and variance

    Let X, Y be independent exponential random variables with means 1 and 2 respectively. Let Z = 1, if X < Y Z = 0, otherwise Find E(X|Z) and V(X|Z). We should first find E(X|Z=z) E(X|Z=z) = integral (from 0 to inf) of xf(x|z). However, how do we find f(x|z) ?
  25. J

    Var of Sum of Random Variables when n is a Random Variable?

    If I have a set of indepenent and identically distributed random variables X1,...Xn, then Var(\sum_{i=1}^{n}X_i) = \sum_{i=1}^{n}Var(X_i). Now I want to know what the sum of variances of Xi would be when n is a random variable? I'm guessing the above statement still holds when n is a random...
  26. J

    Variance Properties: Understanding Var(aX+bY+c) & Solving for Var(aX+bY)

    [SOLVED] Properties of variance Would the Var(aX + bY + c) just be the Var(aX+bY) since adding a single number to the function doesn't change the variance. I would then be able to use the property: Var(aX+bY)= a^2Var(X)+b^2Var(Y)+2abCov(X,Y) Just wondering if anyone can confirm my...
  27. M

    How can we find the variance of S_x, S_y, and S_z?

    Given |Psi> = a|up>+b|down>, in principle it should not be so difficult but when I calculate Delta S=Sqrt[<S^2_x,S^2_y, or S^2_z>-<S_x,S_y, or S_z>^2] the second term gives the problem. Lots of many terms a*, a, b*, b which is not canceled involve. Whoever knows the way to get rid of...
  28. A

    PCA and variance on particular axis

    Hi All: If given a set of 3D points data, it's very easy to calculate the covariance matrix and get the principle axises. And the eigenvalue will be the variance on the principle axis. I have a problem that if given a random direction, how do I calculate the variance of the data on the given...
  29. P

    Stats unknown variance hypothesis testing

    Homework Statement A machine produces metal rods used in an automobile suspension system. A random sample of 12 rods is selected and the diameter is measred.The sample mean is 8.28. and the significance level is 0.05. Is there strong evidence to indicate that mean rod diameter is not 8.20 mm...
  30. Simfish

    Help with variance sum + correlation coefficient formula

    [SOLVED] Help with variance sum + correlation coefficient formula This is a worked example The objective is to prove -1 \leq \rho(X,Y) \leq 1 Then the book uses this formula... (2) 0 \leq Var(\left \frac{X}{\sigma_x} + \frac{Y}{\sigma_y} \right) (3) = \frac{Var(X)}{{\sigma_x}^2} +...
  31. C

    Compute Variance of Random Variable X

    Homework Statement Compute the variance of the random variable X given by V(X) = \sqrt{E((X-E(X))^2)} where E(X) is the expectation value of random variable X Homework Equations Hint: Use parameter differentiation The Attempt at a Solution I have no idea what to do here. I've never taken...
  32. Simfish

    Genetic Variance Between Pops as compared Within Pops

    As it often said, the majority of the variation in the human genome is due to intra-group variation, not inter-group variation (I think .85 is the number due to intra-group variation). I know what this intuitively means, but can anyone explain to me what it rigorously means? (in statistical terms?)
  33. T

    How to Calculate Mean & Variance of a Function

    Can anybody explain to me how to get the mean and the Variance for a specific function. Thanks alot.
  34. marcus

    Surrogate Cosmic Variance Comment thread

    the Cosmic Variance blog has changed format and eliminated a nice feature that used to keep discussion threads alive. on the righthand margin of front page, it used to list which posts had recent comments and, in small font, WHO THE COMMENTERS WERE so if some interesting people, such as Lee...
  35. D

    Variance Analysis using MINITAB

    Homework Statement I'm doing a course in applied mathematical statistics and am having problems with an assignment. I just wanted to check if there was somebody here who could help me with some variance analysis in MINITAB before I post my problem and work (I have to translate the assignment...
  36. B

    Variance and goodness of fit tests

    I'm trying to see how well my data fit a certain probability distribution (an exponential distribution) and I basically want to know how reliable is it to compare the the theoretical variance of the distribution and the variance of the data, to assess the goodness of fit of data to a...
  37. marcus

    Sad disconnect at Cosmic Variance blog-how not to discuss

    Sad disconnect at Cosmic Variance blog---how not to discuss Cosmic Variance blog is known for lively discussion but I just noticed a sad disconnect where the key point Lee Smolin was making just slipped by in a "yes it is---no it isn't" kind of way without any reasoned counterargument. It is...
  38. A

    Solving Variance Problem - Hi All

    Hi all: If I have a dataset V of the size n*1. Assume that the mean of the dataset is 0 and var(V)=x is its variance. If I want to modify this dataset so that the variance of the new dataset will be var(V_hat)=y. The errors are spreaded average on each element in the dataset. What I did is...
  39. T

    Expression in terms of X for the variance

    1. 'Find an expression in terms of x for the variance of: 9,4,x,3' Give your answer in the form of ax^2 + bx + c I would usually give you some information of how I could possibly tackle this question but unfortunately I have no idea. Could someone shed some light? Thanks
  40. J

    Does Sampling Variance Converge to Theoretical Variance in Simulations?

    if a random variable X has variance sigma, does it mean that the average variance of X will be sigma, or will X always have variance sigma. So if I did 10 simulations of the random variable X, is it plausiable that the variances differ widely, but the average of the variances converge to the...
  41. E

    Finding Variance of Sample Mean of Poisson Distribution

    How do I approach finding variance of sample mean of Poisson distribution? thanks.
  42. I

    Solved: Mean & Variance: Find E(Y), Var(Y) of |tan(X)|, cot(X)

    I'm having a problem with my answer for a question involving finding the mean and variance of a function. I'll state the question and list the steps I did so maybe you guys can see where I went wrong. The question is: Given Y = |tan(X)| and X is uniformly distributed on (-pi/2, pi/2) Find a)...
  43. B

    Deriving the Formula for Variance of Variance in Sample Data

    Hopefully someone will be able to help me. I am trying to derive the formula for variance of variance for a sample. This would be similar to variance of a sample mean which is sigma/sqrt(N). I know the variance of sample variance is sigma^2 * sqrt (2) / N, but I can't prove it...
  44. B

    Probability Distribution of 4 Balls: Mean & Variance

    an urn contains 4 red balls and 4 white balls an experiment consists of selecting at random a sample of 4 balls and recording the number of red balls in the sample setup the probability distribution and compute its mean and variance i know what a probablity distribution is. can someone please...
  45. D

    Failure of Levene's test for equality of variance

    Hey all, I am currently working on the statistics part of my Master thesis and I am conducting an ANOVA test to compare mean variances between three samples. Four out of the 15 compared variables do not satisfy Levene's test for equality of variance.:cry: I know that ANOVA is relatively...
  46. F

    If variance is 0, then p(x=c) = 1 c is constant

    I think it is easy but I can't figure it out. :( any help?
  47. P

    Calculating Variance of Variance Estimator for Normal Distribution

    Does anyone know how to calculate the variance of the variance estimator of normal distribution? x_i, i\in\{1,2,...,n\} are n samples of normal distribtuion N(\mu, \sigma^2). And S^2 = \frac{n}{n-1} \sum_i (x_i - \bar x)^2 is the variance estimator, where \bar x = \frac{1}{n} \sum_i x_i...
  48. G

    How Do You Calculate Var(X) in a Conditional Variance Problem?

    the discrete prob distribution X/Y - G - D 0 - 0,1 - 0,15 1 - 0,1 - 0,3 2 - 0,05 - 0,3 this is what i have so far: E[X|Y=D]=0,2 E[X|Y=g]=0,9 E[X]=0,725 E[X^2|Y=D]=0,3 E[X^2|Y=G]=1,5 Var(X|Y=G)=0,69 Var(X|Y=D)=0,26 i.e. [X]=0,2*0,25 + 0,9*0,75=0,725 is the previous...
  49. A

    How Does Variance Relate to Plastic Sheet Bending Angles?

    OK, I am having no problem with the concepts here but just with a particular problem. I have analyzed this problem to bits and nothing is working. Here is what we have: The bending capabilities of plastic sheets are investigated by bending sheets at increasingly large angles until a deformity...
  50. A

    Statistics -> Variance and Linear Combinations

    Having a lot of trouble with a particular problem in the topic of variance. The problem is: "Suppose you are organizing a game where you charge players $2 to roll two dice and then you pay them the difference in scores. What is the variance in your profit from each game? If you are playing a...
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