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Find the standard deviation of the first n natural numbers.

Solution:

It is given: set of first natural numbers

We now need to find the standard deviation

Provided first natural numbers, it can be written in table as shown below

   

Therefore, sums of these are

And

So, we can write the standard deviation as,

Substitute the values

Simplify

Multiplyi the numerator

Take LCM and simplify

As a result, is the standard deviation of the first natural numbers.