Question

what is the variance of first 11 natural numbers ?

Answer 1

Answer:

Step-by-step explanation:

First natural no. are:

X 1 2 3 4 5 6 7 8 9 10 11

N = 11;

Mean of the numbers = ∑Xi/N = 6 (Here i = 1 to 11)

Variance^2 = ∑(X-Mean)^2/N;

Variance^2 = 396.11/11 = 36.01;

Variance = 6.00

Answer 2

Answer:

Varince of first 11 natural numbers is 10

Step-by-step explanation:

Formula used:

Standard deviation of first 'n' natural numbers $=\sqrt{\frac{n^2-1}{12}}$

Variance of first 'n' natural numbers$=\frac{n^2-1}{12}$

Now,

Varince of first 11 natural numbers

$= \frac{n^2-1}{12}\\\\=\frac{(11)^2-1}{12}\\\\=\frac{121-1}{12}\\\\=\frac{120}{12}\\\\=10$