Constant-Mean-Return Model The mean return for the asset i can be The reason is that the latter do not – in general – reduce significantly the variance High Ros in the market model imply low variance levels of the abnormal return. ↑ Bias–variance decomposition. In: Encyclopedia of Machine Learning. Eds. Claude Sammut, Geoffrey I. Webb. Springer S. – ↑. Mean“ (bold number) and Variance (white box) " 1 = essential; 2 = import.; value creation perspective show a high level of unanimous answers (low variance).
Übersetzung für "Varianz," im EnglischVariance estimation has become a priority as more and more Commission it could mean that the chosen estimator is dramatically bad (with very low reliability). Constant-Mean-Return Model The mean return for the asset i can be The reason is that the latter do not – in general – reduce significantly the variance High Ros in the market model imply low variance levels of the abnormal return. Many translated example sentences containing "show low variance" – German-English dictionary the sceptics show a negative variance from the average [ ].
What Does Low Variance Mean Your Answer VideoStandard Deviation - Explained and Visualized
What does variance mean in mathematics? Does low variance lead to high inter rater reliability? Can variance be negative?
When a coin is tossed four time then mean and variance of the number of the head? What is the significance of variance in statistics? Is variance based on deviations from the mean?
A fair coin is tossed 10 times what are the expected mean and variance of the number of heads? What is the sample variance with the mean of How is standard deviation found?
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Trending Questions. Obviously this analogy does not cover the full nuance of the concept of variance. There are a lot of things that need explained, such as why we often use a denominator of n-1 to estimate the population parameter, instead of simply using n.
But as a basic concept to peg the rest of a detailed understanding of variance to, simply drawing it out so I could see it helped immensely.
It helps understand what we mean when we say that variance is the average squared deviation from the mean. It also helps in understanding just what relationship SD has to that average.
I think the key phrase to use when explaining both variance and standard deviation is "measure of spread". In the most basic language, the variance and standard deviation tell us how well spread out the data is.
To be a little more accurate, although still addressing the layman, they tell us how well the data is spread out around the mean.
In passing, note that the mean is a "measure of location". To conclude the explanation to the layman, it ought to be highlighted that the standard deviation is expressed in the same units as the data we're working with and that it is for this reason that we take the square root of the variance.
I think that brief explanation would do the trick. It's probably somewhat similar to an introductory textbook explanation anyway.
I regard the variance of distribution as the moment of inertia with the axis that at the mean of the distribution and each mass as 1.
This intuition would make the abstract concept concrete. Reference: A first course of probability 8th edition.
Sign up to join this community. The best answers are voted up and rise to the top. Asked 9 years, 2 months ago. Active 11 months ago.
Viewed 64k times. PhD PhD Having several time the same question even if here the context is different reduces the average quality of answers.
I want to be able to articulate this concept to people who wouldn't know anything about it and it takes a long while to do so and hence the question.
I see a lot of assumptions being made and almost every answer ends with something that needs to be interpreted. I'm not complaining, just trying to point that out.
I too can't answer the question simply. Maybe it's too difficult? The question, as I interpret it, is more about variance as a number, when is it considered large or small.
The top answer below for example, addresses the question what large variance vs small variance means. Active Oldest Votes. See below: The particular image above is from Encyclopedia of Machine Learning , and the reference within the image is Moore and McCabe's "Introduction to the Practice of Statistics".
EDIT: Here's an exercise that I believe is pretty intuitive: Take a deck of cards out of the box , and drop the deck from a height of about 1 foot.
Hossein Rahimi 1 1 gold badge 2 2 silver badges 8 8 bronze badges. If someone would see the the statistical variance of the darts on the board, what would they conclude?
The number of hands required to remove the darts from the board all at once increases as variance of the dart positions increases Note: very informal argument here as there a number of counterexamples, such as when 3 darts are grouped together and the last dart is on the wall 3 feet from the darboard.
It just hit me! Nice exercise! Suppose for variance or standard deviation the following joke is quite useful: Joke Once two statistician of height 4 feet and 5 feet have to cross a river of AVERAGE depth 3 feet.
You can easily cross the river" I am assuming that layman know about 'average' term. What are they missing that is 'variance' to decide "what to do in the situation?
Biostat Biostat 1, 2 2 gold badges 19 19 silver badges 21 21 bronze badges. But I don't think I understand what is meant by "what to do in the situation"?
What 'exactly' should one do if they have an idea of the variance? How should one interpret it? If you know the variance or SD then you could decide it easily.
Suppose variance is 0. If variance is 4 then better to not cross the river. By the way, just enjoy jokes here stats. I got it! Of this test there are several variants known.
Other tests of the equality of variances include the Box test , the Box—Anderson test and the Moses test. Resampling methods, which include the bootstrap and the jackknife , may be used to test the equality of variances.
The term variance was first introduced by Ronald Fisher in his paper The Correlation Between Relatives on the Supposition of Mendelian Inheritance : .
The great body of available statistics show us that the deviations of a human measurement from its mean follow very closely the Normal Law of Errors , and, therefore, that the variability may be uniformly measured by the standard deviation corresponding to the square root of the mean square error.
It is therefore desirable in analysing the causes of variability to deal with the square of the standard deviation as the measure of variability.
We shall term this quantity the Variance The variance of a probability distribution is analogous to the moment of inertia in classical mechanics of a corresponding mass distribution along a line, with respect to rotation about its center of mass.
This difference between moment of inertia in physics and in statistics is clear for points that are gathered along a line.
Suppose many points are close to the x axis and distributed along it. The covariance matrix might look like. That is, there is the most variance in the x direction.
Physicists would consider this to have a low moment about the x axis so the moment-of-inertia tensor is.
For skewed distributions, the semivariance can provide additional information that a variance does not. The result is a positive semi-definite square matrix , commonly referred to as the variance-covariance matrix or simply as the covariance matrix.
The generalized variance can be shown to be related to the multidimensional scatter of points around their mean. A different generalization is obtained by considering the Euclidean distance between the random variable and its mean.
From Wikipedia, the free encyclopedia. Statistical measure of how far values spread from their average. This article is about the mathematical concept.
For other uses, see Variance disambiguation. See also: Sum of normally distributed random variables. Not to be confused with Weighted variance. See also: Unbiased estimation of standard deviation.
A frequency distribution is constructed. The centroid of the distribution gives its mean. A square with sides equal to the difference of each value from the mean is formed for each value.
Mathematics portal. Some new deformation formulas about variance and covariance. Proceedings of 4th International Conference on Modelling, Identification and Control ICMIC Applied Multivariate Statistical Analysis.
Prentice Hall. December Journal of the American Statistical Association. International Journal of Pure and Applied Mathematics 21 3 : Part Two.
Van Nostrand Company, Inc. Princeton: New Jersey. Springer-Verlag, New York. Sample Variance Distribution. MathWorld—A Wolfram Web Resource.
Journal of Mathematical Inequalities. Encyclopedia of Statistical Sciences. Wiley Online Library. Theory of probability distributions.
Outline Index. Descriptive statistics. Mean arithmetic geometric harmonic Median Mode. Variance Standard deviation Coefficient of variation Percentile Range Interquartile range.
For instance, when calculating a sample variance to estimate a population variance, the denominator of the variance equation becomes N - 1 so that the estimation is unbiased and does not underestimate the population variance.
Statisticians use variance to see how individual numbers relate to each other within a data set, rather than using broader mathematical techniques such as arranging numbers into quartiles.
The advantage of variance is that it treats all deviations from the mean the same regardless of their direction. The squared deviations cannot sum to zero and give the appearance of no variability at all in the data.
One drawback to variance, though, is that it gives added weight to outliers. These are the numbers that are far from the mean. Squaring these numbers can skew the data.
Another pitfall of using variance is that it is not easily interpreted. Users often employ it primarily to take the square root of its value, which indicates the standard deviation of the data set.
As noted above, investors can use standard deviation to assess how consistent returns are over time. In some cases, risk or volatility may be expressed as a standard deviation rather than a variance because the former is often more easily interpreted.
Here's a hypothetical example to demonstrate how variance works. Taking the square root of the variance yields the standard deviation of Financial Analysis.
Advanced Technical Analysis Concepts. Fundamental Analysis.