I understood the formulas, but did not understand why variance is required.
What it denotes. If I say variance is 2.9, then what is 2.9 referring to.
What does that 2.9 say?
Hello again, Petar!
Variance values don’t mean much in itself. So, 2.9 won’t mean anything if you can’t compare it with something.
But think about this.
You have two very popular measures of dispersion – variance and standard deviation. I assume you understand how standard deviation is interpreted, and are asking – why do we need variance if standard deviation is so easily interpretable.
Here’s the detailed answer.
Theoretically, variance makes much more sense. It takes part in describing distributions and has important properties with other measures. An example you will be able to get after watching this course is: the covariance of x and x (so the covariance of the same variable) = Cov (x,x) = Var (x) , or the variance of x.
Standard deviation and correlation are derivative concepts from the bigger ones (variance and covariance). And while for all practical purposes we use standard deviation and correlation, for all theoretical purposes, variance and covariance are much better.
A very theoretical example:
In mathematics (mainly physics and probability), the moment is a quantitative measure, describing the shape of a set of points and is very widely adopted in academia. The central moment is the moment around the mean.
The zeroth central moment is the total probability (one), the first central moment is 0. Because the first moment around the mean itself is 0 (no moment)*. The second central moment is variance, third -> skewness, and the fourth – kurtosis.
*By the way, the first moment (not central) is the mean.
So, based on the theory academia has developed throughout the years, variance is the measure which occurs naturally. Therefore, it has stuck as the main measure of variability in theory (where you don’t care about the units of measurement).
Hope this helps!
The 365 Team