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The red population has mean 100 and variance 100 (SD=10) while the blue population has mean 100 and variance 2500 (SD=50) where SD stands for Standard Deviation. In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.
This follows from the fact that the variance and mean are independent of the ordering of x. Scale invariance: c v (x) = c v (αx) where α is a real number. [22] Population independence – If {x,x} is the list x appended to itself, then c v ({x,x}) = c v (x). This follows from the fact that the variance and mean both obey this principle.
Variation predictable probabilistically; Irregular variation within a historical experience base; and; Lack of significance in individual high or low values. The outcomes of a perfectly balanced roulette wheel are a good example of common-cause variation. Common-cause variation is the noise within the system.
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1] Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered.
In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation of a given data set. Often, variation is quantified as variance; then, the more specific term explained variance can be used. The complementary part of the total variation is called unexplained or residual variation; likewise ...
Plot with random data showing heteroscedasticity: The variance of the y-values of the dots increases with increasing values of x. In statistics, a sequence of random variables is homoscedastic (/ ˌ h oʊ m oʊ s k ə ˈ d æ s t ɪ k /) if all its random variables have the same finite variance; this is also known as homogeneity of variance ...
Positive deviations indicate values above the mean, while negative deviations indicate values below the mean. [1] The sum of squared deviations is a key component in the calculation of variance, another measure of the spread or dispersion of a data set. Variance is calculated by averaging the squared deviations.
Magnetic variation, difference between magnetic north and true north, measured as an angle; p-variation in mathematical analysis, a family of seminorms of functions; Coefficient of variation in probability theory and statistics, a standardized measure of dispersion of a probability distribution or frequency distribution