**Given information:**

- Mean of 5 observations = 5
- Variance of the 5 observations = 124
- Three of the observations are 1, 2, and 6

**To find:**

The mean deviation from the mean of the data.

**Solution:**

**Step 1: Find the sum of the 5 observations**

Since the mean of the 5 observations is given as 5, we can find the sum of the observations using the formula:

Sum of observations = Mean × Number of observations

Sum of observations = 5 × 5 = 25

**Step 2: Find the sum of the remaining two observations**

Out of the five observations, we already know three of them (1, 2, and 6). Therefore, we need to find the sum of the remaining two observations.

Sum of the remaining two observations = Sum of all observations - Sum of three known observations

Sum of the remaining two observations = 25 - (1 + 2 + 6) = 25 - 9 = 16

**Step 3: Find the sum of squares of the five observations**

We know that the variance is the average of the sum of squares of the deviations from the mean. Therefore, we can use the formula:

Variance = (Sum of squares of deviations from the mean) / Number of observations

Since the variance is given as 124 and the number of observations is 5, we can rearrange the formula to find the sum of squares of the deviations from the mean:

Sum of squares of deviations from the mean = Variance × Number of observations

Sum of squares of deviations from the mean = 124 × 5 = 620

**Step 4: Find the sum of squares of the deviations of the known observations from the mean**

We can find the sum of squares of the deviations of the known observations (1, 2, and 6) from the mean using the formula:

Sum of squares of deviations of known observations from the mean = (Observation - Mean)^2 + (Observation - Mean)^2 + (Observation - Mean)^2

Sum of squares of deviations of known observations from the mean = (1 - 5)^2 + (2 - 5)^2 + (6 - 5)^2 = 16 + 9 + 1 = 26

**Step 5: Find the sum of squares of the deviations of the unknown observations from the mean**

To find the sum of squares of the deviations of the unknown observations from the mean, we can use the formula:

Sum of squares of deviations of unknown observations from the mean = Sum of squares of deviations from the mean - Sum of squares of deviations of known observations from the mean

Sum of squares of deviations of unknown observations from the mean = 620 - 26 = 594

**Step 6: Find the unknown observations**

We know the sum of the remaining two observations (16) and the sum of squares of the deviations of the unknown observations from the mean (594). We can use these values to find the unknown observations using the following equations:

Sum of unknown observations = 16
Sum of squares of unknown observations = 594

Let the two unknown observations be x and y. Therefore, we have the following equations:

x + y = 16 (Equation 1)
x^2 + y^2 =