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Measure of dispersion
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- Variance is a measure of dispersion. It is equal to the average squared distance of the realizations of a random variable from its expected value.
www.statlect.com/fundamentals-of-probability/varianceVariance | Definition based on the expected value - Statlect
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Apr 24, 2022 · In both cases, \( f \) is the probability density function of \( X \). Variance is always nonnegative, since it's the expected value of a nonnegative random variable. Moreover, any random variable that really is random (not a constant) will have strictly positive variance.
- Variance
The variance is the probability weighted average of the...
- Variance
- Understanding The Definition
- An Equivalent Definition
- Example
- How to Cite
To better understand the definition of variance, we can break up its calculation in several steps: 1. compute the expected value of , denoted by 2. construct a new random variable equal to the deviation of from its expected value; 3. take the square which is a measure of distance of from its expected value (the further is from , the larger ); 4. fi...
Variance can also be equivalently defined by the following important formula: This formula also makes clear that variance exists and is well-defined only as long as and exist and are well-defined. We will use this formula very often and we will refer to it, for brevity's sake, as variance formula.
The following example shows how to compute the variance of a discrete random variable using both the definition and the variance formula above. The exercisesat the bottom of this page provide more examples of how variance is computed.
Please cite as: Taboga, Marco (2021). "Variance", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/fundamentals-of-probability/variance.
Sep 3, 2021 · The variance is simply the sum of the values in the third column. Thus, we would calculate it as: σ2 = .3785 + .0689 + .1059 + .2643 + .1301 = 0.9475. The following examples show how to calculate the variance of a probability distribution in a few other scenarios.
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance.
The variance is a measure of how spread out the distribution of a random variable is. Here, the variance of Y is quite small since its distribution is concentrated at a single value, while the variance of X will be larger since its distribution is more spread out.
The variance is the probability weighted average of the square of these variances. The square of the error treats positive and negative variations alike, and it weights large variations more heavily than smaller ones.
Variance is a statistic that is used to measure deviation in a probability distribution. Deviation is the tendency of outcomes to differ from the expected value. Studying variance allows one to quantify how much variability is in a probability distribution. Probability distributions that have outcomes that vary wildly will have a large variance.
