If the data x_{1},x_{2},\cdots ,x_{10} is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is : 


 

  • Option 1)

    4 

  • Option 2)

     2\sqrt{2} 

  • Option 3)

      \sqrt{2} 

  • Option 4)

     2

 

Answers (1)

x_{1}+x_{2}+x_{3}+x_{4}=44\cdots \cdots \cdots \cdots (1)

x_{5}+x_{26}+\cdots +x_{10}=96\cdots \cdots \cdots \cdots (2)

\bar{x}=\frac{44+96}{10}=14

\sum x_{i}=44+96=140

Variance  \sigma ^{2}=\frac{\sum x_{i}^{2}}{n}-\bar{x}^{2}=4

standard deviation =\sigma

                              =2


Option 1)

4 

Option 2)

 2\sqrt{2} 

Option 3)

  \sqrt{2} 

Option 4)

 2

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