Is there any reason why the standard deviation is the square root of the variance?
Refer the explanation section.
For a given series, deviations are computed form the mean
The sum total of this deviations will be always zero.
The sum total of positive values are cancelled the sum total of the negative values.
We are unable to find the average deviations.
Ignoring the sign is not scientific.
To do away with the sign, we square all the deviations.
We sum it and divided it by the number of observations.
You have doubled the deviations.
To get back the original average deviation, you have to compute the root.