In a series of 2n observations , half of them equal a and remaining half equal - a . If the standard deviation of the observations is 2, then `|a|` equals

Options

A. `(1)/(n)`
B. `sqrt(2)`
C. `2`
D. `(sqrt(2))/(n)`

Answer

C

Explanation

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`