Variance and Standard Deviation and Covariance.
Variance:
Variance is defined as how far the data is from its average value, in other words variance specifies or tells how the data is dispersed around its mean value.
So Variance is the ratio of sum of squared distance between the observed value to the population mean to the total population size.
Variance is calculated by using the below formula,
Standard Deviation:
Standard Deviation is very much similar to Variance, Standard Deviation is simply the Square root of Variance.
Variance tells us how far the data points are from their mean, whereas Standard Deviation tells us about the concentration of data points around the mean value.
If the Variance of a certain data is 36, then the Standard deviation is 6.
Square root of 36 is 6, so Standard Deviation is 6.
Now let us understand how these concepts are used to analyze the data.
Suppose if the Variance is 0, it says that the data is Identical, if the Variance is high then we say that the data is widely spread and is not Identical.
The more spread the data, the more variance is in relation to the mean.
Low measure of Standard Deviation tells us that large part of the data is surrounded around the mean, where as the large measure of data tells us very small amount of data is surrounded around its mean.
Covariance:
Covariance is the measure of joint variability of two different random variables, in other words Covariance is used to measure how much two variables change in tandem.
Basically, covariance finds out how well two different random variables relates to each other. Covariance is computed by using below formula:
If two variables relate in the same direction then the covariance is positive, where as if they both relate in opposite direction then it is negative.
Covariance only says whether if the variables are similar or not similar, it doesn’t say how much they are similar.