Hello, why is it that the formula of Standard deviation (of both grouped and ungrouped data ) differs in different sources

Question

For instance, the formula for standard deviation of UNGROUPED data in some books is $\sigma={\sqrt {\frac {\sum(x-{\bar X})^{2}}{n}}}$ while in some books, they subtract 1 from the n (number of items in the data set) i.e $\sigma={\sqrt {\frac {\sum(x-{\bar X̄})^{2}}{n - 1}}}$ am a bit confused, what exactly is the major difference between the two

Answer 1

If you're calculating the standard deviation of a known discrete probability distribution (e.g., your $x$s are possible dice rolls), you divide by $n$.

If the distribution is unknown and you're trying to estimate the underlying standard deviation based on data you collected, you divide by $n-1$.

But if you have a lot of data -- so $n$ is very large -- the difference between $n$ and $n-1$ is negligible, so you might as well divide by $n$.