Question

If the sd of the 1st n natural numbers is 2, then the value of n must be

Answer 1

The standard deviation of n natural numbers = sqrt [1/12 (n^2 - 1)] 
Therefore, 
sqrt [1/12 (n^2 - 1)] = 2 
on squaring both sides 
1/12 ( n^2 - 1) = 4 
On multiplying both sides by 12 
n^2 - 1 = 48 
n2 = 48 + 1 = 49 
n = sqrt 49 = 7 
The value of n = 7

Answer 2

Given:

First n natural numbers

Standard deviation=2

To find:

The value of n

Solution:

The value of n is 7.

We know that the given standard deviation of the first n natural numbers can be calculated by taking the root of ($n^{2}$-1)/12.

The number of terms=n

The value of the standard deviation=2

Using the values,

2=$\sqrt{(n^{2}-1)/12 }$

On squaring both sides,

4=$n^{2}$-1/12

4×12=$n^{2}$-1

48+1=$n^{2}$

49=$n^{2}$

7=n

So, the standard deviation of the first 7 natural numbers is 2.

Therefore, the value of n is 7.