Question

What is the variance of first 10 natural numbers

Answer 1

Answer:

The standard deviation of first 10 natural numbers is 8.25.

Answer 2

Answer:

Variance of first 10 natural number is $8.25$.

Step-by-step explanation:

To find variance of first 10 natural number.

The first 10 natural numbers are $1,2,...,10.$

Recall: Variance $=\sum{x^{2} / n}-\left(\sum{x / n}\right)^{2}$

Also $\sum x=1+2+3+\ldots+n=n\left(\frac{n+1}{2}\right)$

And $\sum x^{2}=n(n+1) \frac{(2 n+1)}{6}$

So, $\sum{x}=10(\frac{10+1}{2} )$

             $=55$

$\sum{x^{2}} =\frac{10(10+1)(20+1)}{6}$

        $=385$

So,$\text{Variance}=\frac{385}{10}-(\frac{55}{10} )^{2}$

                  $=38.5-30.25\\=8.25$

Hence, variance of first 10 natural number is $8.25$.

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