If the mean of $4,7,2,8,6$ and $k$ is 7 . Then the mean deviation from the mean of these observations is

The mean of the observations $4, 7, 2, 8, 6, k$ is given as $7$.

$\dfrac{4 + 7 + 2 + 8 + 6 + k}{6} = 7$

$\dfrac{27 + k}{6} = 7$

$27 + k = 42$

$k = 42 - 27 = 15$

The observations are $4, 7, 2, 8, 6, 15$. The mean is $\bar{x} = 7$.

The mean deviation from the mean is given by $\dfrac{1}{n} \sum_{i=1}^{n} |x_i - \bar{x}|$.

Mean deviation $= \dfrac{|4-7| + |7-7| + |2-7| + |8-7| + |6-7| + |15-7|}{6}$

Mean deviation $= \dfrac{|-3| + |0| + |-5| + |1| + |-1| + |8|}{6}$

Mean deviation $= \dfrac{3 + 0 + 5 + 1 + 1 + 8}{6} = \dfrac{18}{6} = 3$.

Answer: 3