Mean Value Theorem

is continuous in
and differentiable in as its derivative
Now,

Now, according to Lagrange's theorem, there exist a point such that

Let the five observations be , and . The mean of the five observations is given by: Substituting the known values: This simplifies to: Thus, So the sum of the other two observations is 11. Next, the variance is given by: Substituting the known values, the variance is 5.2: Simplifying the terms: Now, we know that . Let's substitute and , which satisfies both the conditions: Thus, the other two observations are and .