Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$Var={\delta }^2=\frac{\sum x_i^2}{n}-{\mu }^2\text{Standard Deviation}=\sqrt{\frac{2^2+3^1+a^2+{11}^2}{4}-{\left(\frac{2+3+a+11}{4}\right)}^2}=3.5\Rightarrow \frac{134+a^2}{4}-{\left(\frac{16+1}{4}\right)}^2=(3.5{)}^2\frac{4(134+a^2)}{16}-\frac{({16}^2+a^2+32a)}{16}=(3.5{)}^{2}536+4a^2-256-a^2-32a=1963a^2-32a+84=0$