Verified Solution • 2025–26 Session moderate

QJEEM19Ma54f7: JEE Main 2019 Mathematics - Class 11 JEEM19Ma54f7 Solution: If mean and standard deviation of 5 observations x 1 , x 2 , x…

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

Multiple Choice Options

  • A 582.5
  • B 507.5
  • C 586.5
  • D 509.5

Step-by-Step Verified Solution

x‾=10⇒∑i=15xi=50\overline x = 10 \Rightarrow \sum\limits_{i = 1}^5 {{x_i} = 50}

S.D.   =∑i=15xi25−(x‾)2=8= \sqrt {{{\sum\limits_{i = 1}^5 {x_i^2} } \over 5} - {{\left( {\overline x } \right)}^2}} = 8

⇒ ∑i=15(xi)2=109\Rightarrow \,\sum\limits_{i = 1}^5 {{{\left( {{x_i}} \right)}^2}} = 109

variance =  ∑i=15(xi)2+(−50)26−(∑i=15xi−506)= \,\,{{\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= \,\,507.5

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