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In a series of 2n observations, half of...

In a series of `2n` observations, half of them equal `a` end remaining half equal `-a.` If the S.D. of the observationsis `2,` then `|a|` equals
(1) `1/n`
(2) `sqrt2`
(3) `2`
(4) `sqrt2/n`

A

`(1)/(n)`

B

`sqrt(2)`

C

`2`

D

`(sqrt(2))/(n)`

Text Solution

Verified by Experts

The correct Answer is:
C
In the 2n observations, half of them equal to a and the remaining half equal to -a. Then the mean of total 2n observations is equal to zero. Therefore,
`S.D.=sqrt((sum(x-x)^(2))/(N))`
`2=sqrt((sum x^(2))/(2n))`
`implies 4 =(sum x^(2))/(2n) implies 4=(2a^(2))/(2n) implies a^(2)=4`
`implies |a|=2`
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