Answer:
For a data set of N elements:
{x₁, x₂, ..., xₙ}
The mean is:
[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]
The mean absolute deviation is:
[tex]MAD = \frac{|x_1 - M| + ... + |x_n - M|}{N}[/tex]
And the population standard deviation is:
[tex]PSD = \frac{\sqrt{|x_1 - M|^2 + ... + |x_n - M|^2} }{\sqrt{N}}[/tex]
In this case, our set has 5 elements, and the set is:
{2, 4, 6, 9, 14}
The mean of this set is:
[tex]M = \frac{2 + 4 + 6 + 9 + 14}{5} = 7[/tex]
The mean absolute deviation is:
[tex]MAD = \frac{|2 - 7| + |4 - 7| + |6 - 7|+ |9 - 7| + |14 - 7| }{5} = 3.6[/tex]
And the population standard deviation is:
[tex]PSD = \sqrt{\frac{|2 - 7|^2 + |4 - 7|^2 + |6 - 7|^2+ |9 - 7|^2 + |14 - 7|^2 }{5}} = 4.2[/tex]
