I do not understand the statement below. I think it's an easy rule that I overlook. I understand how you read the average, but how do you determine the standard deviation?
The graphs all show the normal probability density function.
It is stated that graph 1 has an average of 10 and standard deviation 2.
On
The function has the form $f(x) = \frac 1{\sqrt{2\pi}\sigma}\,e^{-\frac{(x-\mu)^2}{2\sigma^2}}$. The maximum of the curve is at $x=\mu$ and has the value $f(\mu) = \frac 1{\sqrt{2\pi}\sigma}$. In the picture you can read off $f(\mu)$. So you just have to solve for $\sigma$, which gives $\sigma = \frac 1{\sqrt{2\pi}f(\mu)}\approx \frac{1}{2.5\cdot f(\mu)}$.
For example for graph no. 2 you have $f(\mu) = 0.4$, so $\sigma\approx\frac{1}{2.5\cdot 0.4}=1$.
Consider a normal:
The height at a peak is:
$$\frac{1}{\sqrt{2 \pi} \sigma}$$
The height at the point one standard deviation away from the peak is
$$\frac{1}{\sqrt{2 \pi}\sigma} e^{-1/2}$$
So find the point that is $e^{1/2} \approx .606$ the height of the peak. The difference between its $x$ value and $\mu$ is $\sigma$.