Covariance and variance are often employed in statistics as mathematical concepts, although in spite of similar-sounding names, their implications are completely distinct. Covariance is the measure of how two random variables jointly vary and the correlation between variables is calculated.
The variance however refers to the distribution of the data set, for example, the distance between numbers and the mean. Variance is especially valuable in determining the likelihood of future events or performances which we may calculate online by using a variance math calculator.
Therefore, in this article, the variance, as well as covariance, are discussed briefly to comprehend them separately.
Table of Contents
Variance
By definition, a variance is a number that shows how far-off a number’s set could lie apart. The variance is the same as the standard deviation being squared and hence the same things are expressed but in a different manner.
Bringing a measure of central tendency, the variance measures a data set’s dispersion from the center of the set’s distribution. The bigger the difference, the more the values are spread apart. The smaller the covariance is, the values will be more congested.
Variance Calculations
Variance is determined as the arithmetically mean or average of each value’s squared difference of the sample or population arithmetic mean. The difference is squared, so that greater deviations from the mean can be more deviated.
Because variation is a squared difference, it is most of the time difficult to convey meaningfully. The standard deviation is usually reported as the square root of the variance, as stated in the same unit as the data.
A less variance implies that the data points are relatively near to each other and also to the average. However, a large variation shows a large dispersion of the data points between them and the average.
As the variance is the average distance between the square points and also the mean. Moreover, the variance allows departures to be considered equally in both directions i.e. The positive errors are treated the same as negative ones.
Covariance
Covariance is a measure of how much two random variables vary jointly according to probability theory and statistics. There is a specific formula for calculating covariance but the covariance between x and y calculator is the best-recommended tool to do it. The covariance is further subdivided into two types, the positive and the negative.
The covariance is positive if the increase in the value of one variable correlates to an increase in other variable. And in the same values the decrease in values occurs, that is, the variables tend to have similar behavior. On the contrary situation, the covariance is negative, if the larger values of one variable cause the smaller values of the other, i.e. when the variables tend to display opposite behavior.
Therefore, the sign of covariance reflects the trend in the linear connection of the variables. The covariance’s magnitude cannot be interpreted easily. However, its magnitude reflects the strength of the linearity in the normalized form of the covariance which is the correlation coefficient.
There must be a distinction between two random variables. These are the population parameter that may be considered to be the property of the joint distribution of probabilities, and sample covariance, which acts as the parameter’s estimated value.
Does covariance have to be positive
As discussed above there are two subtypes of covariance i.e. the positive covariance and the negative covariance. Depending upon the correlation that both the variables form they can either forma positive or negative covariance.
The relation among two variables that is formed as a result of increase or decrease in one variable and correlates with the increase or decrease in another variable respectively is positive covariance.
The negative covariance does exist, in contrast to positive covariance. The in negative covariance increase in variable causes decrease in other variables. Therefore, in negative covariance the variables behave in contrast to each other.
As the covariance forms a negative correlation among its variables sometimes. Hence it is not necessary for the covariance to be positive always. The covariance forms either positive and even negative correlations with its variables.
