JEE Main202116 Mar 2021Morning ShiftMathematicsStatisticsActual
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?
Options
- Ab 2 = 3 a 2 + c 2 + 9 d 2
- Bb 2 = a 2 + c 2 + 3 d 2
- Cb 2 = 3 a 2 + c 2 + d 2
- Db 2 = 3 a 2 + c 2 - 9 d 2
Correct answer
D. b 2 = 3 a 2 + c 2 - 9 d 2
Step-by-step solution
For a , b , c mean = a + b + c 3 = x ¯ b = a + c ⇒ x ¯ = 2 b 3 . . . ( 1 ) S . D . a + 2 , b + 2 , c + 2 = S . D . a , b , c = d ⇒ d 2 = a 2 + b 2 + c 2 3 - x ¯ 2 ⇒ d 2 = a 2 + b 2 + c 2 3 - 4 b 2 9 ⇒ 9 d 2 = 3 a 2 + b 2 + c 2 - 4 b 2 ⇒ b 2 = 3 a 2 + c 2 - 9 d 2