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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)

$2$

Views

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

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

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

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

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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