Question

The mean and standard deviation of $1,2,3,4,5,6$ is

• A. $\frac{7}{2},\frac{35}{12}$
• B. $\frac{7}{2},\sqrt{3}$
• C. $\frac{7}{2},\sqrt{\frac{35}{12}}$
• D. $3,3$

Answer 1

The correct option is C $\frac{7}{2},\sqrt{\frac{35}{12}}$

$\overline{x}=\frac{\sum x_i}{n}\Rightarrow \overline{x}=\frac{1+2+3+4+5+6}{6}\Rightarrow \overline{x}=\frac{7}{2}$
Now,
${\sigma }^2=\frac{\sum _{i=1}^n{x}_i^2}{n}-(\overline{x}{)}^2\Rightarrow {\sigma }^2=\frac{1+4+9+16+25+36}{6}-\frac{49}{4}\Rightarrow {\sigma }^2=\frac{35}{12}\therefore \sigma =\sqrt{\frac{35}{12}}$