What is the standard deviation of the frequency table below?

Question

Hello, I have some issues with finding the standard deviation of this question. I found the mean as 337.5 km, and I considered that standard deviation is the root of the variance. I first squared the frequency to calculate E($X^2$) and subtracted by $mean^2$. Then I square rooted and got 80.6 km as my variance, but looks like it is wrong. Can someone find my mistake?

Answer 1

$$E(X^2)=\frac{2•50^2+5•150^2+\cdots}{2+5+\cdots}\\ \sigma^2=E(X^2)-(E(X))^2\\ \sigma=\sqrt{\sigma^2}$$

I think $80$km is a reasonable value for $\sigma$