The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3, and 8, then what is the ratio of the other two observations?

Let the two observations be x₁ and x₂.
Mean = Σxi/5 = 5
=> 1 + 3 + 8 + x₁ + x₂ = 25
=> x₁ + x₂ = 13 (1)
Variance (σ²) = Σ(xi²)/5 - (Σxi/5)² = 9.20
=> Σxi² = 171
=> 1² + 3² + 8² + x₁² + x₂² = 171
=> x₁² + x₂² = 97. (2)
From (1) and (2),
(x₁ + x₂)² - 2x₁x₂ = 97
(13)² - 2x₁x₂ = 97
169 - 2x₁x₂ = 97
2x₁x₂ = 72
x₁x₂ = 36
Therefore, the ratio x₁:x₂ = 4:9.