Question

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

• A. $3a^2-23a+44=0$
• B. $3a^2-26a+55=0$
• C. $3a^2-32a+84=0$
• D. $3a^2-34a+91=0$

Answer 1

The correct option is C $3a^2-32a+84=0$

Standard deviation is given as,
$\sigma =\sqrt{\frac{\sum x_i^2}{n}-(\overline{x}{)}^2}$

Mean, $\overline{x}=\frac{16+a}{4}$

$\Rightarrow {\sigma }^2=\frac{\sum x_i^2}{n}-(\overline{x}{)}^2$
$\Rightarrow {\left(\frac{7}{2}\right)}^2=\frac{4+9+a^2+11}{4}-{\left(\frac{16+a}{4}\right)}^2$
$\Rightarrow 3a^2-32a+84=0$