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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? |
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Answer» `(sqrt23)/(3)` `(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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