Question

The mean and S.D. of $1,2,3,4,5,6$is

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

Answer 1

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

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