1. Standard deviation from graph

Sorry if this is a stupid question but please give me some help
How would you know the standard deviation of a graph just from looking at it, I get that the mean is 10 but how is the standard deviation 4/3?

2. Re: Standard deviation from graph

I guess there is no actual method to deduct the standard deviation just by observing the graph IMO. However, you can use following trick to roughly estimate the SD from a Normal distribution.
It is known that $\text{Pr}(x\in[\mu-3\sigma,\mu+3\sigma])\approx 0.95$ where $\mu$ and $\sigma$ are the mean and SD.
Basically, if you could guess where the tail almost become zero from the figure, it helps you to make a rough estimation.
In you figure, $\mu=10$ and tails almost disappear at $x<6$ and $x>14$. Therefore, $10+3\sigma=14$ and $10-3\sigma=6$ need to satisfied.
That says $\sigma \approx 4/3$.