Question

If the data $x_1,x_2,....,x_{10}$ 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 :

• A. $4$
• B. $2$
• C. $2\sqrt{2}$
• D. $\sqrt{2}$

Answer 1

The correct option is B $2$

Given $\frac{x_1+x_2+x_3+x_4}{4}=11\Rightarrow x_1+x_2+x_3+x_4=44$

and $\frac{x_5+x_6+x_7+...+x_{10}}{6}=16\Rightarrow x_5+x_6+x_7+...+x_{10}=96$
Therefore, mean of complete data $\overline{X}=\frac{x_1+x_2+....+x_{10}}{10}=\frac{44+96}{10}\Rightarrow \overline{X}=14$

$\because \sum X_i^2=2000$
Therefore, Variance $=\frac{2000}{10}-{14}^2=200-196=4$
And hence, standard deviation $=\sqrt{\text{variance}}=\sqrt{4}=2$