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For (2n+1) observations `x_(1), -x_(1),x_(2),-x_(2),..,x_(n),-x_(n)` and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true ?

A

1.`SD lt MD`

B

2.`SD gt MD`

C

3.SD=MD

D

4.Nothing can be said in general about the relationship between SD and MD

Text Solution

Verified by Experts

The correct Answer is:
B
On arranging the given observations in ascending order, we get All negative terms `ubrace(" 0 ")_((n+1)^(th)"term")` All positive terms
Median of given observations =(n+1)th term=0
`therefore SD gt MD`
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