Question

find the variance of first 10 natural number ​

Answer 1

Step-by-step explanation:

var (1,2,3.........n)=10 (given)

formula {σ

2

=

N

∑f

i

d

i

2

−(

N

∑f

i

d

i

)

2

⇒

n

1

2

+2

2

+−−−−−−−−+n

2

+(

2

n+1

)

2

=10

⇒

2

n+1

[

3

2n+1

−

2

n+1

]=10

⇒

2

n+1

[

6

4n+2−3n−3

]=10

⇒

2

n+1

[

6

n−1

]=10

⇒n

2

−1=120

⇒n=11

and,

var(2,4,6........2m)=16

⇒4var(1,2,3..........,m)=16

⇒var(1,2,3........,m)=4

⇒

12

m

2

−1

=4

⇒m

2

−1=48

⇒m=7

∴m+n=11+7=18