standard deviation of multiple vectors

Question

I have multiple vectors of length N, and I want to calculate the standard deviation (Std) of them, so if I have these vectors:

[1.03132, 1.456758,1.1324684]
[0.46546, 3.232658,3.1456444]
[0.21346, 0.568748,1.5554487]

The standard deviation vector is:

[0.34198709 1.10748961 0.86669951]

If I want the final value as a single value rather than a vector, can I calculate again the Std of the produced vector again!?

Is this the right way to deal with vectors to get the Std ?! if no, how can I do that?

Answer 1

The standard deviation measures how far from the average something is.

If you take the standard deviation of the entries of your result vector, you'll get a number that indicates how far each coordinate's standard deviation is from the average of your result vector's coordinates.

So for instance, if you result vector were something like $v =[10,10,10]\,$ (meaning your input vectors have high variance) and you took the standard deviation of the coordinates of $v$, you'd get $0$.

In short, I don't think this is a good measure.