∵∑i=118​(xi​−β)2=90 and ∑i=118​(xi​−β)=∑i=118​(xi​−α)+18(α−β) =36+18(α−β) So Var(xi​)=Var(xi​−β)=18∑(xi​−β)2​−(18∑(xi​−β)​)2 ​⇒1=1890​−(2+α−β)2⇒2+α−β=±2⇒α−β=0,−4​ ∵ α and β are distinct, so ∣α−β∣=4