If the data

Question:

If the data $\mathrm{x}_{1}, \mathrm{x}_{2}, \ldots . \mathrm{x}_{10}$ 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 :

  1. 4

  2. 2

  3. $\sqrt{2}$

  4. $2 \sqrt{2}$


Correct Option: , 2

Solution:

$\mathrm{x}_{1}+\ldots+\mathrm{x}_{4}=44$

$\mathrm{x}_{5}+\ldots+\mathrm{x}_{10}=96$

$\overline{\mathrm{x}}=14, \Sigma \mathrm{x}_{\mathrm{i}}=140$

Variance $=\frac{\sum \mathrm{x}_{\mathrm{i}}^{2}}{\mathrm{n}}-\overline{\mathrm{x}}^{2}=4$

Standard deviation $=2$

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