If the standard deviations of the numbers 2,3,a and 11 is 3.5 then which of the following is true?

$mean\overline{x}=\frac{{\displaystyle \sum x_i}}{n}=\frac{2+3+a+11}{4}=\frac{16+a}{4}=4+\frac{a}{4}$

S.D=3.5   $\Rightarrow S.D=\frac{35}{10}$

$\Rightarrow \mathrm{var}iance=\frac{49}{4}$

$\Rightarrow \frac{{\displaystyle \sum {x_i}^2}}{n}-{\left(\frac{{\displaystyle \sum x_i}}{n}\right)}^2=\frac{49}{4}$

$\Rightarrow \frac{4+9+a^2+121}{4}-{\left(\frac{a}{4}+4\right)}^2=\frac{49}{4}$

$\Rightarrow \frac{134+a^2}{4}-\frac{a^2+256+32a}{16}=\frac{49}{4}$

$\Rightarrow \frac{536+4a^2-a^2-256-32a}{16}=\frac{49}{4}$

$\Rightarrow 3a^2-32a+280=196$

$\Rightarrow 3a^2-32a+280-196=0$

$\Rightarrow 3a^2-32a+84=0$