FOr the interpretation of the variance, it is the fluctuation of the data around the mean. So if I know that mean (say mean=0), and then there are lots of data (70%) points are greater than +/-10 away from the mean, then I probability can tell the variance.
However, how can I tell the variance by looking at the pdf only (without using the direct computation)? Unlike above, the pdf doesn't give the number of data points, it gives the probability of those data points. Can I assume that, pdf(x=x0)=high probability, then that x0 signifies the locations where the majority of the data points are located?
Hint: note that $$ \text{Var}(X)=E[(X-E(X))^2]=E(X^2)-[E(X)]^2=E(X^2) $$ provided that $E(X)=0$, which is the case for your situation. So the variance is just the expectation of $X^2$. Therefore, if you already know how to compare $E(X)$ by looking at the pictures, just apply the same technique but for $E(X^2)$.