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The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -

JEE · Math · previous-year question

  1. A.6 : 7
  2. B.10 : 3
  3. C.4 : 9correct
  4. D.5 : 8

Answer

C. 4 : 9

Explanation

Let two observations are x1 & x2 mean = $${{\sum {{x_i}} } \over 5} = 5 $$ $$\Rightarrow 1 + 3 + 8 + {x_1} + {x_2} = 25$$ $$ \Rightarrow {x_1} + {x_2} = 13$$ . . . . (1) variance $$\left( {{\sigma ^2}} \right)$$ = $${{\sum {x_i^2} } \over 5} - 25 = 9.20$$ $$ \Rightarrow $$ $${\sum {x_i^2 = 171} }$$ $$ \Rightarrow $$ $$x_1^2 + x_2^2 = 97$$ . . . . . (2) $$ \Rightarrow $$(x1 + x2)2 $$-$$ 2x1x2 = 97 $$ \Rightarrow $$ 169 - 2x1x2 = 97 or x1x2 = 36 $$ \therefore $$ x1 : x2 = 4 : 9

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