Exams › JEE Advanced › Maths
Three observations a, b, c satisfy b = a + c. If the standard deviation of the set {a+2, b+2, c+2} equals d, which of the following relations holds?
- b² = 3(a² + c²) + 9d²
- b² = a² + c² + 3d²
- b² = 3(a² + c² + d²)
- b² = 3(a² + c²) - 9d²
Correct answer: b² = 3(a² + c²) - 9d²
Solution
The variance of {a+2, b+2, c+2} equals the variance of {a, b, c} since shifting by 2 does not affect spread. With b = a+c the variance works out to d² = (a² + c² - ac)/3, leading to 3(a²+c²) - 9d² = 3ac + a² + c² = (a+c)² = b².
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