KVPY2013MathematicsStatistics
Let n 3 . A list of numbers 0 < x₁ < x₂ < < x_ n has mean and standard deviatiion . A new list of numbers is made as follows : y₁=0, y₂=x₂, , y_ n-1 =x_ n-1 , y_ n =x₁+x_ n . The mean and the standard deviation of the new list are and . Which of the following is necessarily true?
Options
- A= ,
- B= ,
- C=
- Dmay or may not be equal to
Correct answer
A. = ,
Step-by-step solution
= 0+x₂+x₃ x_ n-1 + (x₁+x_ n ) n = ²= 1 n y_ i ²- ²= 1 n [0²+x₂²+x₃² (x_ n-1 )²+ (x₁+x_ n )² ]- ² ²- ²= 2 x₁ x_ n n >0 so >