If the standard deviation of the numbers 2,3 , $2 x$ and 11 is 3.5. Find the possible values of $x$.

Question

Aicharya · Accepted Answer

$\sigma=3.5$ $\begin{gathered} \text {Mean }(\bar{x})=\frac{2+3+2 x+11}{4}=\left(4+\frac{x}{2}\right) \ \sigma^2=\frac{1}{n} \sum\left(x_i-\bar{x}\right)^2 \ \Rightarrow \quad(3 \cdot 5)^2=\frac{1}{4}\left[\left(-2-\frac{x}{2}\right)^2+\left(-1-\frac{x}{2}\right)^2+\left(\frac{3 x}{2}-4\right)^2+\left(7-\frac{x}{2}\right)^2\right] \ \Rightarrow 3 x^2-16 x+21=0 \Rightarrow x=\frac{7}{3}, 3 \end{gathered}$

If the standard deviation of the numbers 2,3 , \(2 x\) and 11 is 3.5. Find the possible values of \(x\).

Solution