I am looking for the concept about how to estimate standard deviation.

Actually I'm not sure how can I get a concept the estimate standard deviation ?

If you know the concept, then would you let me know it here?

Also if you have any reference or examples, it will be help to me.

p.s. Is this different between "estimate standard deviation" and "estimated standard deviation" ? I think it seems to the same.

Updated

What does different between "Method of Least Squares" and "estimate standard deviation"?

Are those the same concept? I don't know estimate standard deviation.

Given data ${ \left\{ {x}_{i} \right\} }_{i = 1}^{N}$ the Empirical STD of the data is well defined:
$$STD = \sqrt{ \frac{1}{N - 1} \sum_{i = 1}^{N} { \left( {x}_{i} - \bar{x} \right) }^{2} }$$
Where $\bar{x}$ is the empirical mean of the data given by:
$$\bar{x} = \frac{1}{N} \sum_{i = 1}^{N} {x}_{i}$$