Multiple choice

If the standard deviation of 10 observations ${x_{1\,\,}}{x_2}\,,\,....\,\,{x_{10}}$ is $4$ that of another set of $10$ observations ${y_{1\,\,}}{y_2}\,,\,....\,\,{y_{10}}$ is $3$ and also ${X_i}\, = \,\left( {{x_i}\, - \,\overline x } \right)\,\left( {{y_i}\, - \,\overline y } \right)\,,\,\overrightarrow x $ is mean of all $x_{ i }^{ 's }\ $ and $y$ is mean of all $y_{ i }^{ 's }\,\sum\limits_{i = 1}^{10} {{X_i}} \, = \,80 $ then standard deviation of ten observation $\left( {{x_1}\, - \,{y_1}} \right)\,,\,\left( {{x_2}\, - \,{y_2}} \right)\,,.......\left( {{x_{10}}\, - {y_{10}}} \right)$ is

  1. $1$
  2. $3$
  3. $5$
  4. $\sqrt 5 $
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D Correct answer