Statistics Part 1

Step -1: Find n using variance of first n natural number is .
var(1,2,3,...,n)=10
Using formula for variance we have,
‌⇒‌

12+22+...+n2

n

−(‌

1+2+...+n

n

)2=10
[‌ Since, ‌‌σ2=‌

Σfidi

N

−(‌

Σfidi

N

)2]
‌⇒‌

(n+1)(2n+1)

6

−(‌

n+1

2

)2=10
‌⇒‌

n2−1

12

=10
‌⇒n2−1=120
‌⇒n2=121
‌⇒n=11
Step -2: The variance of the first m even natural number:
⇒var(2,4,6...2m)=16
⇒22‌var(1,2,...,m)=16
⇒var(1,2,...,m)=‌

16

22

=4
⇒‌

m2−1

12

=4
⇒m2−1=48
⇒m2=49
⇒m=7
Step -3: Evaluate m+n.
m+n=7+11
⇒m+n=18.
The value of m+n=18.