# What's the meaning of $\sigma^3$ and $\sigma^4$ and how to find them

I know you can use $$\sigma^3$$ and $$\sigma^4$$ with $$\mu$$3 and $$\mu$$4 respectively to find the skewness and the kurtosis, but by themselves what do they mean + what's the formula to find them?

Thank you in advance!

## 1 Answer

skewness=$$\frac{\mu_3}{\sigma^3}$$, kurtosis=$$\frac{\mu_4}{\sigma^4}$$, where $$\mu_k=E((X-\mu)^k)$$ and $$\sigma^2=E((X-\mu)^2)=E(X^2)-\mu^2$$

Using Google:

https://brownmath.com/stat/shape.htm