If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respecti…

Question

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, \ldots .., x5 and --50 is equal to

Accepted Answer

$$\overline x  = 10 \Rightarrow \sum\limits_{i = 1}^5 {{x_i} = 50} $$

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 $$ = \,\,{{\sum\limits_{i = 1}^5 {{{\left( {{x_i}} \right)}^2}}  + {{\left( { - 50} \right)}^2}} \over 6} - \left( {\sum\limits_{i = 1}^5 {{{{x_i} - 50} \over 6}} } \right)$$

$$ = \,\,507.5$$

Solutions · 1