Let X_1, X_2, …, X_18 be eighteen observations such that Σ_i=1^18(X_i-α)=36 and Σ_i=1^18(X_i-β)^2=90, where α and β are distinct real numbers. If the…

Let $\displaystyle X_1, X_2, \ldots, X_{18}$ be eighteen observations such that $\displaystyle \sum_{i=1}^{18}\left(X_i-\alpha\right)=36$ and $\displaystyle \sum_{i=1}^{18}\left(X_i-\beta\right)^2=90$, where $\displaystyle \alpha$ and $\displaystyle \beta$ are distinct real numbers. If the standard deviation of these observations is $\displaystyle 1$, then the value of $\displaystyle |\alpha-\beta|$ is \_\_\_\_.