Standard Deviation is square root of variance. It is a measure of the extent to which data varies from the mean.
Standard Deviation (for above data) = √4 = 2
Why did mathematicians chose square and then square root to find deviation, why not simply take difference of values?
One reason is the sum of differences becomes 0 according to definition of mean. Sum of absolute differences could be an option, but with absolute differences it was difficult to prove many nice theorems.
Some Interesting Facts:
1) Value of standard deviation is 0 if all entries in input are same.
2) If we add (or subtract) a number say 7 to all values in input set, mean is increased (or decreased) by 7, but standard deviation doesn’t change.
3) If we multiply all values in input set by a number 7, both mean and standard deviation are multiplied by 7. But if we multiply all input values with a negative number say -7, mean is multiplied by -7, but standard deviation is multiplied by 7.