Variance refers to the average of the squared deviations of a random variable, taking its mean value.
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 is used to identify the mean of the quadratic deviations of a random variable , considering its average 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 that variable considered in relation to 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 square kilometers.
It is worth noting that measures of dispersion (also known as measures of variability ) 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 measure of dispersion, the greater the variability. On the other hand, the lower the value, the greater the homogeneity.
Utility of variance
What variance does is establish the variability of the random variable. It is important to note that, in certain cases, it is preferable to use other dispersion measures given the characteristics of the distributions.
Sample variance is the calculation of the variance of a community, group or population based on a sample. Covariance , on the other hand, is the measure of the 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 to be partitioned into different components.
Analysis of variance can be important when testing a theory.
The standard or typical deviation
One of the most important concepts related to variance is the standard deviation, also known as typical deviation, which represents the magnitude of the dispersion of interval and ratio variables, and is very useful in the field of descriptive statistics . To obtain it, one simply starts with the variance and calculates its square root .
In practice, if we have the values (expressed in millimetres) 14mm, 11mm, 10mm, 6mm and 4mm, we can calculate their average by adding them up and dividing the result by 5, which is the number of elements. We would obtain 9mm. To find the variance, we would have to subtract each of the values from the mean just shown, square each result (to avoid negative numbers affecting the study), add them together and, finally, divide everything by 5. The variance is 93.8 square millimetres. Finally, to find the standard deviation, we calculate the square root, which leaves us with 9.68mm (note that the unit is again millimetres).
These data are very useful and necessary for analyzing and describing information , since 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 those simply subjected to their arithmetic average.
Variance in theory testing
In the process of testing a theory, it is important to anticipate possible results, and deviation serves to analyze the behavior of values around their average . It establishes new points that open doors to different classifications and data that may not have been considered at first.
Using only the average of a set of values, it is not possible to know if any of them is excessively far from the "normality" existing in that context. The standard deviation allows us to establish two new limits around this central line, to know when an element is too small or large.