For a,b,c
mean =3a+b+c(=xˉ)
b=a+c
⇒xˉ=32b ...(1)
S.D.(a+2,b+2,c+2)=S.D.(a,b,c)=d
⇒d2=3a2+b2+c2−(xˉ)2
⇒d2=3a2+b2+c2−94b2
⇒9d2=3(a2+b2+c2)−4b2
⇒b2=3(a2+c2)−9d2
Consider three observations a,b and c such that b=a+c. If the standard deviation of a+2,c+2 is d, then which of the following is true?
Held on 16 Mar 2021 · Verified 6 Jul 2026.
b2=3(a2+c2)+9d2
b2=a2+c2+3d2
b2=3(a2+c2+d2)
b2=3(a2+c2)−9d2
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