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Consider three observations \(a, b\) and \(c\) such that \(b=a+c\). If the standard deviation of \(a+2, b+2, c+2\) is \(…

Q1

Consider three observations \(a, b\) and \(c\) such that \(b=a+c\). If the standard deviation of \(a+2, b+2, c+2\) is \(d\), then which of the following is true?

[JEE Main 2021, 16 Mar (Shift 1)]

a

\(b^2=3\left(a^2+c^2\right)-9 d^2\)

b

\(b^2=a^2+c^2+3 d^2\)

c

\(b^2=3\left(a^2+c^2+d^2\right)\)

d

\(b^2=3\left(a^2+c^2\right)+9 d^2\)

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