# 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). – Szabolcs Nov 20 '13 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 '13 at 0:43