Question

Variance Of First 20 Natural Numbers Is_____

Answer 1

Answer:

Step-by-step explanation:

Variance of first n natural numbers is =  

n

∑(x  

i

​  

)  

2

 

​  

−(Mean)  

2

 

=  

n

1  

2

+2  

2

+3  

2

.....n  

2

 

​  

−(  

2

n+1

​  

)  

2

 

σ  

2

=  

6n

n(n+1)(2n+1)

​  

−  

4

(n+1)  

2

 

​  

 

σ  

2

=  

12

n  

2

−1

​  

 

​  

 

So variance of first 20 natural number

=σ  

2

=  

12

20  

2

−1

​  

=  

12

399

​  

=  

4

133

​