The outcome of each of 30 items was observed, 10 items gave an outcome `(1)/(2)-d` each, 10 items gave outcome `(1)/(2)` each and the remaining 10 items gave outcome `(1)/(2) + d` each. If the variance of this outcome data is `(4)/(3)`, then `|d|` equals

Options

A. 2
B. `sqrt5/2`
C. `sqrt2`
D. `2/3`

Answer

C

Explanation

10 items gave outcome = `(1/2-d)`
10 items gave outcome = `1/2`
10 items gave outcome =`(1/2+d)`
Mean`(barx)=(10xx(1/2-d)+10xx1/2+10(1/2+d))/30=15/30=1/2`
`Sigma(x_i^2)=10(1/2-d)^2+10xx(1/2)^2+10xx(1/2+d)^2`
`=10(1/4+d^2-d)+10xx1/4+10(1/4+d^2+d)=30/4+20d^2`
Variance `(sigma^2)=((Sigmax^2-((Sigmax)^2)/n))/n`
`rArr 4/3=((15/2+20d^2)-30xx1/4)/30rArr 40=20d^2 rArr d=pmsqrt2rArr |d|=sqrt2`