Step-by-step Solution:

First, find the missing two observations using the given mean and variance. Then, calculate the mean deviation.
Step 1: Find the sum of all observations
The sum of the 5 observations is: \[ 5 \times 5 = 25 \] Step 2: Find the sum of the two unknown observations
The sum of the known observations is: \[ 1 + 2 + 6 = 9 \] The sum of the two unknown observations is: \[ 25 - 9 = 16 \] Let the two unknown observations be \( x_1 \) and \( x_2 \): \[ x_1 + x_2 = 16 \] Step 3: Use the variance to find the sum of the squares of all observations
The variance formula: \[ \sigma^2 = \frac{\sum_{i=1}^{n}x_i^2}{n} - \bar{x}^2 \] Plugging in the given values: \[ 12.4 = \frac{\sum_{i=1}^{5}x_i^2}{5} - 5^2 \] \[ \frac{\sum_{i=1}^{5}x_i^2}{5} = 12.4 + 25 = 37.4 \] \[ \sum_{i=1}^{5}x_i^2 = 37.4 \times 5 = 187 \] Step 4: Find the sum of the squares of the two unknown observations The sum of squares of the known observations: \[ 1^2 + 2^2 + 6^2 = 1 + 4 + 36 = 41 \] The sum of the squares of the two unknown observations: \[ 187 - 41 = 146 \] \[ x_1^2 + x_2^2 = 146 \] Step 5: Solve for the two unknown observations
We now have two equations:
1. \( x_1 + x_2 = 16 \)
2. \( x_1^2 + x_2^2 = 146 \)
Using the first equation: \[ x_2 = 16 - x_1 \] Substituting into the second equation: \[ x_1^2 + (16 - x_1)^2 = 146 \] \[ x_1^2 + 256 - 32x_1 + x_1^2 = 146 \] \[ 2x_1^2 - 32x_1 + 110 = 0 \] \[ x_1^2 - 16x_1 + 55 = 0 \] \[ (x_1 - 5)(x_1 - 11) = 0 \] \[ x_1 = 5 \quad \text{or} \quad x_1 = 11 \] Thus, the two unknown observations are 5 and 11.
Step 6: Calculate the Mean Deviation
The observations are: 1, 2, 5, 6, 11.
The formula for mean deviation:
\[ MD = \frac{|1-5| + |2-5| + |5-5| + |6-5| + |11-5|}{5} \] \[ MD = \frac{4 + 3 + 0 + 1 + 6}{5} \] \[ MD = \frac{14}{5} = 2.8 \] The mean deviation from the mean of the data is 2.8.