# Graphical representation of variance

I'm learning statistics and I can imagine pretty well what the standard deviation looks like (image here).

But, knowing that the standard deviation is the square root of the variance, I just can't figure out what that looks like.

Can anybody provide me with an illustration or a plot to help me understand that?

• You are approaching this the wrong way. A graphical representation is not always the best way to look at things. Variance is just the square of the standard deviation, which you already understand. A better question is: why is the square interesting enough that it has its own name? The answer to that is that variances are additive (while standard deviation is not). Nov 20, 2013 at 17:31
• Thanks for your replies. I do understand that the variance represents the dispersion of the values, and that the standard deviation includes 68.2% of the values in normally distributed, nominal number sets. Therefore, it must be interesting enough beecause it should kind of represent the area of the Gaußian distribution, but I can not calculate this area precisely. That's why I would like to understand that visually. Do you refer to 'additive' because the formula you provided (Bienaymé) doesn't contain the sum of(each value minus the difference to the average)^2 divided by (n-1) part? Thanks
– nic
Nov 21, 2013 at 0:43