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.