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 $2000,$ then the standard deviation of the 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 $\frac{x_5+x_6+x_7+\cdots +x_{10}}{6}=16$
$\Rightarrow x_5+x_6+x_7+\cdots +x_{10}=96$

Therefore, mean of complete data,
$\overline{X}=\frac{x_1+x_2+\cdots +x_{10}}{10}=\frac{44+96}{10}\Rightarrow \overline{X}=14$

Since $\sum X_i^2=2000,$
therefore variance $=\frac{2000}{10}-{14}^2=200-196=4$
Hence, standard deviation $=\sqrt{\text{variance}}=\sqrt{4}=2$