Consider 10 observations x_1, x_2, …, x_10 such that Σ_i=1^10(x_i-α)=2 and Σ_i=1^10(x_i-β)^2=40, where α, β are positive integers. Let the mean and…

Consider $\displaystyle 10$ observations $\displaystyle x_1, x_2, \ldots, x_{10}$ such that $\displaystyle \sum_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\displaystyle \sum_{i=1}^{10}\left(x_i-\beta\right)^2=40$, where $\displaystyle \alpha, \beta$ are positive integers. Let the mean and the variance of the observations be $\displaystyle \frac{6}{5}$ and $\displaystyle \frac{84}{25}$ respectively. Then $\displaystyle \frac{\beta}{\alpha}$ is equal to :