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If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of thefollowing is true ?(1) `3a^2-26 a+55=0`(2) `3a^2-32 a+84=0`(3) `3a^2-34 a+91=0`(4) `3a^2-23 a+44=0`A. `3a^(2)-26a+55=0`B. `3a^(2)-32a+84=0`C. `3a^(2)-34a+91=0`D. `3a^(2)-23a+44=0` |
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Answer» Correct Answer - B We know that, if `x_(1), x_(2), … x_(n)` are n observations, then their standard deviation is given by `sqrt((1)/(n)Sigmax_(i)^(2)-((Sigma_(i))/(n))^(2))` We have, `(3.5)^(2)=(2^(2)+3^(2)+a^(2)+11^(2))/(4)-((2+3+a+11)/(4))^(2)` `rArr (49)/(4)=(4+9+a^(2)+121)/(4)-((16+a)/(4))^(2)` `rArr (49)/(4)=(134+a^(2))/(4)-(256+a^(2)+32a)/(16)` `rArr (49)/(4) = (4a^(2)+536-256-a^(2)-32a)/(16)` `rArr 49 xx 4= 3a^(2) -32a +280 rArr 3a^(2)-32a+84 =0` |
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