JEE Mains · Maths · STD 11 - 13. statistics
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 ?
- 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 \(b ^{2}=3\left( a ^{2}+ c ^{2}\right)-9 d ^{2}\)
Answer & Solution
Correct Answer
(D) \(b ^{2}=3\left( a ^{2}+ c ^{2}\right)-9 d ^{2}\)
Step-by-step Solution
Detailed explanation
For \(a, b, c\) mean \(=\frac{a+b+c}{3}(=\bar{x})\) \(b = a + c\) \(\Rightarrow \quad \bar{x}=\frac{2 b}{3}\) \(.....(1)\) S.D. \((a+2, b+2, c+2)=\) S.D. \((a, b, c)=d\) \(\Rightarrow \quad d ^{2}=\frac{ a ^{2}+ b ^{2}+ c ^{2}}{3}-(\overline{ x })^{2}\)…
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