1.

The mean square deviation of a set of m observationsy_1, y_2…..y_mabout a point K is defined as1/m sum_(i = 1)^(m) (y_2 - k)^(2). The mean square deviation about-3 and 3 are 16 and 8 respectively, then standard deviation of this set of observation?

Answer»

`(sqrt23)/(3)`
`sqrt(7)`
`(sqrt41)/(3)`
`(sqrt(38))/(3)`

SOLUTION :`(1)/(m)SUM(y_(i)+3)^(2)=16"...(i)"`
`(1)/(m)sum(y_(i)-3)^(2)=8"...(ii)"`
`"Adding (i) and (ii)"`
`(1)/(m)sum_(i=l)^(m)(2y_(i)^(2)+18)=24`
`(2)/(m)sum_(i=l)^(m)y_(i)^(2)+18=24""(sum_(i=l)^(m)y_(i)^(2))/(m)=3`
`"Subtracting (i) and (ii)"`
`(12)/(m)sum_(i=l)^(m)y_(i)=8`
`(sum_(i=l)^(m)y_(1))/(m)=(8)/(12)","sigma=sqrt((sumy_(i)^(2))/(m)-((sumy_(i))/(m))^(2))=sqrt(3-((2)/(3))^(2))=sqrt((23)/(9))=(sqrt(23))/(3)`


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