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If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2, ….., x5 and –50 is equal to

JEE · Math · previous-year question

  1. A.582.5
  2. B.507.5correct
  3. C.586.5
  4. D.509.5

Answer

B. 507.5

Explanation

$$\overline x = 10 \Rightarrow \sum\limits_{i = 1}^5 {{x_i} = 50} $$ S.D. $$ = \sqrt {{{\sum\limits_{i = 1}^5 {x_i^2} } \over 5} - {{\left( {\overline x } \right)}^2}} = 8$$ $$ \Rightarrow \,\sum\limits_{i = 1}^5 {{{\left( {{x_i}} \right)}^2}} = 109$$ variance $$ = \,\,{{\sum\limits_{i = 1}^5 {{{\left( {{x_i}} \right)}^2}} + {{\left( { - 50} \right)}^2}} \over 6} - \left( {\sum\limits_{i = 1}^5 {{{{x_i} - 50} \over 6}} } \right)$$ $$ = \,\,507.5$$

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