Given:
- Mean of 5 observations = 4.8
- Variance of 5 observations = 6.16
- Three observations are 2, 3, and 6

To find:
- The remaining two observations

Solution:

Step 1: Find the sum of all five observations

- Mean of 5 observations = (Sum of all observations) / 5
- Sum of all observations = 4.8 * 5 = 24

Step 2: Find the sum of the given three observations

- Sum of 2, 3, and 6 = 2 + 3 + 6 = 11

Step 3: Find the sum of the remaining two observations

- Sum of the remaining two observations = Sum of all observations - Sum of the given three observations
- Sum of the remaining two observations = 24 - 11 = 13

Step 4: Find the variance of the remaining two observations

- Variance of 5 observations = [(Variance of the remaining two observations * 2) + (Variance of the given three observations * 3)] / 5
- 6.16 = [(Variance of the remaining two observations * 2) + (1.555 * 3)] / 5
- Variance of the remaining two observations = 12.05 / 2 = 6.025

Step 5: Find the standard deviation of the remaining two observations

- Standard deviation of the remaining two observations = Square root of variance of the remaining two observations
- Standard deviation of the remaining two observations = Square root of 6.025 = 2.454

Step 6: Find the two observations

- We know that the sum of the two observations is 13
- We also know that their standard deviation is 2.454
- Let's assume that one observation is x, then the other observation will be 13 - x
- We can now use the formula for standard deviation:
- Standard deviation = Square root of [(Observation 1 - Mean)² + (Observation 2 - Mean)²] / 2
- Plugging in the values, we get:
- 2.454 = Square root of [(x - 4.8)² + ((13 - x) - 4.8)²] / 2
- Solving for x, we get:
- x = 3.2 or x = 6.4

Step 7: Final answer

- The two remaining observations are either 3.2 and 9.8 or 6.4 and 6.6.