How to calculate Volatility

[Creatives]

Hello
first of all I would like to apologize for my poor english.
anyway I have the problem.

Wikipedia says:
The annualized volatility

is the standard deviation

of the instrument's logarithmic returns in a year.
The generalized volatility

for time horizon

in years is expressed as:

My question is: why root of T? And I really dont know how to use this formula. Could you explain me " standard deviation

of the instrument's logarythmic " how to calcuate that?

I calculate volatility like this:
I find an arithemtic mean (mean) of set of prices. and standard deviation of total variance.

Thx for response. I would very appreciate it