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Let n ge 3. A list of numbers 0 le x1 l...

Let n `ge ` 3. A list of numbers `0 le x_1 le x_2 le … le x_n` has mean `mu` and standard deviatiion `sigma`. A new list of numbers is made as follows : `y_1 = 0 , y_2 = x_2, …, y_(n-1) = x_(n-1) , y_(n) = x_1 + x_(n)`. The mean and the standard deviation of the new list are `hat(mu) and hat(sigma)`. Which of the following is necessarily true ?

A

`mu=hatmu, sigma le hatsigma`

B

`mu=hatmu, sigma ge hatsigma`

C

`sigma = hatsigma`

D

`mu` may or may not be equal to `hatmu`

Text Solution

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The correct Answer is:
A
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