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 ?
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]
- 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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- [JEE MAIN 2022]
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- [JEE MAIN 2023]
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