What is variance?

The notion of variance is often used in the field of statistics. It is a word promoted by the English mathematician and scientist Ronald Fisher (1890 – 1962) and serves to identify the mean squared deviations of a random variable, considering its mean value.

The variance of random variables, therefore, consists of a measure linked to their dispersion. It is the expectation of the square of the deviation of this considered variable from its mean and is measured in a different unit. For example, in cases where the variable measures a distance in kilometers, its variance is expressed in kilometers squared.

Note that dispersion measures (also identified with the name of variability measures) are responsible for expressing the variability of a distribution by means of a number, in cases where the different scores of the variable are very far from the mean. . . The higher the value of the dispersion measure, the greater the variability. On the other hand, the lower the value, the more homogeneous. What the variance does is establish the variability of the random variable. It is important to remember that, in certain cases, it is preferable to use other measures of dispersion, given the characteristics of the distributions. It is called sample variance when the variance of a community, group or population is calculated based on a sample. The covariate, moreover, is the measure of joint dispersion of a pair of variables. Experts speak of analysis of variance to name the collection of statistical models and their associated procedures in which the variance appears partitioned into different components. The standard or standard deviation One of the most important concepts related to variance is the standard deviation, also known as typical, which represents the magnitude of the dispersion of the range and ratio variables, and is very useful in the field of descriptive statistics. To get it, just start from the variance and calculate its square root. In practice, if we have the values ​​(expressed in millimeters) of 14mm, 11mm, 10mm, 6mm and 4mm, we can calculate their average by adding them together and dividing the result by 5, which is the number of elements. We would have 9 mm. To find out the variance, we must subtract each of the values ​​from the recently evidenced mean, square each result (to avoid negative numbers that affect the study), add them together, and finally divide everything by 5. The variance is 93 , 8 square millimeters. Finally, to find the standard deviation, we compute the square root, which leaves us with 9.68 mm (note that the unit is again millimeters).

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These data are very useful and necessary to analyze and describe information, as they offer us different points of view, as well as different trends in the data that characterize the object in question and allow us to establish more complex and dynamic comparison parameters than mere isolated values. .or simply subject to its arithmetic mean. In the process of testing a theory, it is important to anticipate possible outcomes, and deviation is used to analyze the behavior of values ​​around their mean. It establishes new points that open doors to different classifications and data that may not have been considered initially. If only the average is evaluated between a set of values, it is not possible to know if some of them are excessively detracting from the existing «normality» in that context. The standard deviation allows to establish the new limits around the central line, to know when an element is too small or too big.

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